The government will make a "balanced judgement" when deciding how to relax the coronavirus lockdown, Cabinet Office minister Michael Gove has said.
The government does not yet have the information to show it would be safe to lift the restrictions, he told the BBC's Andrew Marr Show.
It comes as another 596 people have died with the virus, taking total UK hospital deaths to 16,060.
A Sunday Times report said schools could reopen as early as 11 May.
Mr Gove dismissed that as "not true", saying no decision had been made.
He also added that hospitality venues would be among the last to exit the lockdown, which was extended on Thursday for another three weeks.
Strict limits on daily life - such as requiring people to stay at home, shutting many businesses and preventing gatherings of more than two people - were first introduced on 23 March, as the government tried to limit the spread of coronavirus.
Calls for the government to provide an exit plan to end the lockdown have intensified, and some other countries have begun to relax their measures.
Mr Gove said the UK government was taking "a deliberately cautious and measured approach, guided by the science".
He said: "When we have the information, when we have the data that allows us confidently to relax those restrictions we will do so, but that data, that information, is not yet in place."
He also said that while the government was investing in trying to get a vaccine as "quickly as possible" it could not be certain when it would be ready.
"I don't think it's the case that anybody should automatically assume that a vaccine is a dead cert to come soon."
Prof Sarah Gilbert, who is leading a team developing a vaccine at Oxford University, told the BBC's Andrew Marr that they hoped to start clinical trials towards the end of next week but nobody could be sure it was possible "to find a workable vaccine".
She said they would need government support to accelerate manufacturing because the UK currently does not have the facilities to make the vaccine on a large scale.
As the trials progress, she said more people would be vaccinated - including the older population - to look at the safety and immune response of the vaccine.
"That's important because it's the older population that we really need to protect with the vaccine. But with vaccines in general, you get not-so-good immune responses as the immune system ages."
Prof Gilbert added that other coronaviruses have shown scientists that immunity is not usually very long-lived, but there was a difference between immunity acquired after natural infection and immunity acquired after vaccination.
"We could find the vaccine-induced immunity lasts a lot longer than infection-induced immunity," she said.
The Sunday Times article suggested schools could reopen in May as part of the first stage of a three-phase "traffic light" plan, which would see the over-70s and other vulnerable people having to wait until a vaccine was found to be able to resume normal life.
First Minister Nicola Sturgeon has denied claims that lockdown restrictions could be lifted next month, saying that all decisions must be "solidly based and not premature".
Mr Gove was also asked about another wide-ranging report in the same paper which criticised the government's response to the outbreak.
The report said Prime Minister Boris Johnson, who is currently recovering from Covid-19, had missed five meetings of the Cobra emergency committee in the run-up to the outbreak.
Mr Gove said: "He didn't (attend) but then he wouldn't - because most Cobra meetings don't have the prime minister attending them."
He added that it was "grotesque" to portray Mr Johnson "as though not caring about this".
It comes as there have been a further 482 deaths of people diagnosed with Covid-19, according to NHS England, bringing the total number of hospital deaths in England to 14,400.
In Scotland, another 10 people who tested positive for coronavirus have died, according to the Scottish government, taking its total to 903 deaths.
One person in Northern Ireland has died in hospital with coronavirus in the past day, the Public Health Agency has said, bringing the overall number of hospital deaths there to 194.
Another 41 people who tested positive for Covid-19 have died in Wales, Public Health Wales announced on Sunday, taking its total deaths to 575.
BBC health correspondent Nick Triggle said the 596 virus deaths in the UK was the lowest daily figure in nearly two weeks.
But he added: "The fall should be treated with caution, the numbers often drop at weekends because of delays reporting and recording deaths."
The report also said the government ignored calls to order more personal protective equipment (PPE) for healthcare staff, as well as sending some stock to China.
Mr Gove said the UK had sent protective clothing to help China deal with its outbreak, but said Beijing had generously given far more back.
The pledge to take delivery of more PPE came after warnings that some hospitals' intensive care units could run out of gowns over the weekend.
However, a delivery of 84 tonnes of PPE from Turkey which had been due to arrive on Sunday has been delayed.
A government spokesman confirmed the delay, saying they were working "to ensure the shipment is delivered as soon as possible".
The shipment contained only "a few days' supply" anyway, according to Niall Dickson, chief executive of the NHS Confederation which represents hospital trusts.
In other developments:
- Construction of Scotland's temporary coronavirus hospital, NHS Louisa Jordan, has been completed. The £43m facility at the Scottish Events Campus (SEC) in Glasgow will be ready to receive Covid-19 patients from Monday, if required.
- Asda is cancelling a quarter of orders with clothing suppliers and has said it would only pay for part of such cancelled orders
- New data from the National Care Forum has added to growing evidence that the number of deaths linked to coronavirus in UK care homes may be far higher than those recorded so far
- Front-line NHS staff should receive an extra £29-a-day reward for their service during the pandemic, the Liberal Democrats have said
- Some disadvantaged teenagers in England will be able to borrow laptops to help them study at home when schools are closed
- Britons in Bangladesh will be able to fly home this week, with up to 850 seats available on four repatriation flights
- Lady Gaga, Paul McCartney and Billie Eilish were among more than 100 artists to perform from their homes in a globally televised concert, organised to celebrate healthcare workers
Asked whether the government would own up to any errors it had made, Mr Gove said: "All governments make mistakes, including our own. We seek to learn and to improve every day.
"It is the case, I'm sure, at some point in the future, that there will be an opportunity for us to look back, to reflect and to learn some profound lessons."
Shadow health secretary Jonathan Ashworth said there were "serious questions about the government's immediate response to this pandemic and whether they were too slow to act".
"We knew in February how serious this virus was. Yet today our NHS and care staff are still lacking adequate PPE," he added.
The government has appointed Lord Deighton, who headed the Organising Committee of the 2012 London Olympics, to resolve problems with supplies and distribution of PPE.