Britain once looked very different. In place of sheep-strewn fields and treeless uplands, there were vast natural forests, glades and wild spaces. Within them, wolves, bears and lynx roamed the land. The first Britons lived alongside woolly mammoths, great auks and wild cows called aurochs.

All that is now gone. Humans chopped down the trees to make space for farms, and hunted the large animals to extinction, leaving plant-eaters to decimate the country's flora. Britain is now one of the few countries in the world that doesn't have top predators.

No matter how much we may think England's green and pleasant countryside is "natural", it is a pale shadow of what once was – and what could be again.

If some conservationists have their way, parts of the UK could be restored to a truly wild state. This "rewilding" would bring back animals and plants that have been lost, and allow them to roam freely. In these new wild spaces, people could reconnect with animals and plants in a way no park or zoo could ever manage. But it's also a hugely controversial idea.

There are various interpretations of rewilding. The word was coined in 1990 by an American environmentalist named Dave Foreman, who went on to found the Rewilding Institute. Then in 1998, Michael Soulé and Reed Noss set out the core ideas in an article for Wild Earth magazine.

Top predators allow many more species to flourish

The key to rewilding is creating large protected areas in which animals and plants are left to their own devices. The new wildernesses have to be large to support top predators like wolves, which need space and lots of prey.

The top predators are crucial, because they keep down the populations of their prey. These are normally plant-eating animals like deer, which would otherwise run riot and decimate trees and other plant life – and in turn destroy the habitats for many other animals. By keeping plant-eaters in check, top predators allow many more species to flourish.

These ripple effects are called "trophic cascades". Soulé and Noss argued that ecosystems cannot function as they should without top predators or carnivores.

In the last few years, the idea of rewilding parts of the UK has started to gain some support. For instance, the naturalist Chris Packham has spoken out in favour of reintroducing wolves and lynxes.

We have very poor ecosystems

The journalist George Monbiot has also become a passionate supporter of rewilding, which he described in his 2013 book Feral. He says the return of charismatic predators could make Britain's landscape more exciting.

"We have very poor ecosystems," says Monbiot. Although the UK has plenty of designated national parks, they are all dominated by human activities.

The International Union for Conservation of Nature ranks protected areas on a six-point scale, where 1 is the most wild. "None of our national parks are above grade 5," says Monbiot. "That means that they're marginally better than multi-storey car parks for wildlife, but not by much."

In June 2015, Monbiot and other conservationists will launch Rewilding Britain, a new charitable organisation that will champion rewilding.

Rewilding the UK is not a new concept

They aim to set aside three areas of at least 100,000 hectares of land in which ecological processes are dominant. They also want to designate 30% of the UK's seas as no-take zones, so life can return to the oceans.

"We'd love to have some places where you don't have to travel halfway round the world to see magnificent wildlife," says Monbiot.

This may sound very radical. The funny thing is, rewilding the UK is not a new concept. We are arguably doing it already.

Conservation groups like Trees For Life have been busily restoring native forests and other key landscapes for decades. Many of the biggest projects are happening in Scotland, but there are smaller ones elsewhere.

Marshy areas are crucial habitats for many birds

These include The Great Fen Project in east England, The National Forest in central England, Moor Trees in the south-west and the Mid Wales Red Squirrel Project.

The Royal Society for the Protection of Birds, despite its name, spends much of its time rebuilding wetlands, particularly in the eastern county of Essex. These marshy areas are crucial habitats for many birds.

Thanks to the RSPB's efforts, populations of red kites, cirl bunting, great bustards and goshawks have returned to healthy numbers.

The Knepp Castle Estate in West Sussex, which was once a loss-making intensive farm, is now being rewilded. A host of rare species has returned, from nightingales to barbastelle bats, cuckoos and purple emperor butterflies.

But the story that really brought rewilding into the spotlight began in February 2014, when wild beavers turned up in the south-western county of Devon.

A family of three was found living on the River Otter. It was the first time beavers had been found in the wild in England since they were hunted to extinction in the 16th century.

The UK government raised concerns that they could be carrying a tapeworm

It's not clear where the beavers came from, but they might have escaped from captivity, as beavers are often employed as land management on private estates.

When the runaway beavers were discovered, the UK government raised concerns that they could be carrying a tapeworm called Echinococcus multilocularis, which can be harmful for humans, and that the landscape might have changed too much for them to stay.

Environmental groups and local people campaigned for them to be allowed to stay. Eventually the beavers, now five strong, were tested and found to be disease-free. In March 2015, the beavers were re-released for a 5-year trial.

Beavers are cute, but that's not the only reason for letting them return to the UK.

By building dams across rivers, which create ponds and eventually change the rivers into wetlands, they help species to flourish that would otherwise struggle. Birds, amphibians and fish all benefit.

"You get beautiful beaver ponds and dams, which are used by a whole host of species from otters to birds," says Alasdair Cameron of Friends of the Earth, who was involved in campaigning for the beavers to remain.

There is even evidence that beavers could, in a modest way, help prevent dangerous climate change.

Beavers in this country are a fantastic way of sequestering carbon in wetlands

The Earth's rising temperatures are largely driven by carbon dioxide, a greenhouse gas, so the more carbon can be kept out of the atmosphere the better.

"One of the principal sources of carbon is the destruction of soils and wetland ecosystems," says Cameron. "Beavers in this country are a fantastic way of sequestering carbon in wetlands."

There is a second population of around 150 beavers, living on the River Tay in Scotland, probably after being illegally released. In 2015 the National Trust for Scotland, a charity that looks after Scottish heritage, said they should be allowed to remain

But even if that happens, it will only be a tiny step down a very long road.

Compared to other European countries, the UK has been slow to reintroduce its indigenous species, despite European legislation encouraging it.

In many cases we have to pick them up and plonk them down

Big predators now roam in nearly one-third of mainland Europe. There are currently 17,000 brown bears, 12,000 wolves, 9,000 Eurasian lynx and 1,250 wolverines. But not in Britain.

One reason is simple: Britain is an island so it's hard to get to. On the mainland, wolves are spreading freely from the east into the west.

"Wolves come across the border from the Czech Republic or Poland to Germany," says David Hetherington, a biologist who advises the Cairngorms National Park. "They come back under their own steam."

But on their own, wolves aren't going to make it to Britain. "Birds can do that to an extent but mammals need a helping hand from humans," says Hetherington. "In many cases we have to pick them up and plonk them down."

Paul Lister, the owner of Alladale Wilderness Reserve in north-east Scotland, is exploring the possibility of reintroducing wolves and bears. He believes we need predators, and suggests releasing two packs of wolves and 20-odd bears on his own land.

It won't start eating people's livestock and pets

"We got rid of wolves and we've got room to bring them back," says Lister. "It will give the land a chance to recover."

Critics say his plan is unrealistic and naïve, but Lister points out that he is not talking about letting the animals go wherever they like.

"It's not full-blown reintroduction," says Lister. "It won't start eating people's livestock and pets and interrupting our lives, because it will be inside a fence and it will be properly managed."

Even with such controls, reintroducing wolves or bears to the UK is likely to prove difficult, as many people consider them too dangerous to live with. Farmers in particular are deeply opposed.

The Scottish highlands already have high densities of prey animals

But lynx might be more viable. These big cats pose no threat to humans. In March 2015, the Lynx UK Trust announced plans for trial releases.

Hetherington says the Scottish highlands already have high densities of prey animals, enough to support about 400 lynx. There is also plenty of room for the cats, which live in well-wooded landscapes and have large home ranges.

A small habitat network in the south of Scotland could support around 50 lynx, says Hetherington. But it's not something to rush into.

"There needs to be some sensible, inclusive and respectful dialogues involving local communities and sectors who feel threatened by this," says Hetherington. "If that doesn't happen, lynx reintroduction will never be given the go-ahead, or it will fail and you'll get illegal hunting."

We don't know the risks

The main objection to reintroducing lynx, or other big predators, is that it could affect farmers' livestock and livelihoods. "These animals are high-level predators whose reintroduction would directly impact on sheep farmers and related businesses," said the National Sheep Association.

"There's a high degree of uncertainty about how it would play out in Scotland," says Andrew Bauer of the National Farmers Union of Scotland. "We don't know the risks and it's irresponsible to present it as cut-and-dried, as some are… Losing lambs is distressing and damaging for business."

One reintroduction, carried out 40 years ago, illustrates the problems.

White-tailed eagles, also known as sea eagles, are the largest birds of prey in the UK. They were wiped out in the early 20th century, but were then reintroduced on the Isle of Mull.

In conservation terms, they are a success story. As of 2015 there are almost 100 breeding pairs across Scotland, according to Mull Eagle Watch.

Llamas and donkeys can be used to protect sheep

However, their return has caused problems for farmers, because the eagles sometimes kill lambs. Scottish Natural Heritage offers compensation, but Bauer says the programme is flawed.

"The scheme pays farmers to do things that will reduce the risk but it doesn't cover the losses," he says. "The problem is much more serious that we thought because the number of sea eagles is increasing."

If lynx are reintroduced, a similar story may play out. Lynx UK Trust has mentioned plans to compensate farmers but the details are hazy.

The good news is that lynx's impact can be controlled. "You can bring predation down to really low levels," says Hetherington. Llamas and donkeys can be used to protect sheep, and since the lynx live in forests, simply moving lambs away from forest edges keeps them much safer.

Because people need to live off the land, rewilding is not just a scientific issue: it's a political one.

Many of the traditional uses of British land are hopelessly unprofitable anyway

The worry is that reintroducing big predators, or allowing farmland to revert to its natural state, will be bad for the rural economy – which is already struggling. "The sheep farmer has a right to be there," says Bauer.

The counter-argument, put forward by Monbiot, is that many of the traditional uses of British land are hopelessly unprofitable anyway. Many only survive thanks to government subsidies such as the Common Agricultural Policy. In particular, upland areas such as the Welsh hills and Scottish highlands have infertile soils that don't yield much.

Rewilding, says Monbiot, offers alternative sources of income, which might well mean rural areas are better off. One option is eco-tourism, in which people pay to stay in wild areas and to be shown the best places to see the animals. Local people with decades of expertise often make the best guides.

"We are in conversation with quite a few farmers who are actually enthusiastic," says Monbiot.

It is about satisfying a natural human desire: to come face to face with the wild

Even if rewilding doesn't boost rural economies in the way Monbiot thinks it could, there are other potential benefits.

For instance, if Britain's bare hills become cloaked with trees, and trees are also allowed to grow right up next to rivers, they will trap rainwater. This should mean a more steady flow of water into rivers, reducing the risk of both floods and droughts.

But it is also about satisfying a natural human desire: to come face to face with the wild, where our species spent almost all of its history.

"We live in a pretty garden, a sanitised landscape. It's nothing like what it used to be," says Lister.

We have a tremendous capacity for being enchanted by the wonders of nature

For many of us, BBC Earth documentaries are as close as we get to wild nature. Yet there is growing evidence that spending time there is good for both our physical and psychological health.

"We have a tremendous capacity for being enchanted by the wonders of nature and we have very little scope for exercising that capacity in this country," says Monbiot.

With popular figures like Bill Oddie and Chris Packham speaking out in favour of rewilding, there might be some appetite for Britain to become a wilder place again. And if a country as stripped of its wildlife as Britain can do it, anywhere can.