UK property transactions in March 2021 were at their highest level since records began in 2005, according to the HMRC.
There were more than 180,000 UK property sales in March, more than double the number in the same month last year.
Official data shows average UK house prices rose more than 8% in a year.
Kirstie Allsopp, presenter of Channel 4's Location, Location, Location, says she is "concerned" by the decisions people are making.
She says: "People don't know if they're going to have to go back to work in an office.
"People are making big decisions about moving, assuming they won't have the commute anymore, assuming they're going to have the time to spend on a big garden… I worry because they're making big financial decisions based on these lifestyle factors."
BBC Radio 5 Live's Naga Munchetty spoke to four people who have had recent experience of the housing market.
'I'm like a hawk on Rightmove, I refresh it several times an hour'
Kirsty Kirby is a first-time buyer in South Yorkshire who has been planning to move house since 2018.
The 37-year-old pharmaceutical sales representative says prices in 2018 were a little out of her reach, so she decided to "save aggressively" throughout 2019 and was viewing two to three houses a week before the first lockdown. Now she says even getting a viewing for a property is a challenge.
"I ring for many properties," she says, "I'm like a hawk on Rightmove, I must refresh it several times an hour, just to see what's on."
Kirsty says most homes she enquires about already have multiple viewing bookings within minutes of appearing online and estate agents warn her the house will be going to 'best and final' offers.
"Best and final is a system where buyers put in one offer for the seller to choose from, in order to avoid a bidding war between prospective home-owners.
Kirsty says, in her experience, anytime a property goes to best and final "it goes way above the asking price because people get crazy".
"Technically I can wait to buy my house, but that's painful because I've been planning this for a long time," she says.
'I'm ready to go'
Seema Devchand is a 30-year-old first-time buyer in Manchester who had an offer accepted on a house in June 2020, but has yet to complete.
The HR advisor says the couple she's buying from have struggled to find anywhere to buy, so she's been waiting patiently for ten months.
"I'm ready to go," she says. "I'm ready to complete but they haven't found anything, so I don't know if they've just got cold feet because they're a retired couple.
"I've been really lenient, I'm in a fortunate situation where I'm living with parents, but I can't even look at another house because the market is crazy. I can't even get a viewing."
Seema is buying the house by herself and, despite trying hard to save over the past two years, says her budget "isn't big, so I'm up against a lot of foreigners and investors, which no one talks about".
"My worry is it doesn't calm down because people have saved a lot from being at home. People have got more to play with, especially couples."
'We didn't want to play people off against each other'
Mark Goodall, a 58-year-old Covid infection study worker, was selling his parents' house as his father had gone into a care home. He says he and his sister were "surprised" by the demand with offers on the first viewings.
"By the end of that day we'd already had a couple of offers, then after the Easter weekend we picked up some more," he says.
Mark and his sister decided to accept an offer which was £12,000 over the asking price from a couple with no chain, before receiving an offer from a second couple £28,000 over the asking price.
Mark and his sister didn't want to "play people off against each other" but that the price difference would pay for three months of care for their parents, who are both in care homes.
They ultimately ended up negotiating with the first couple, who ended up paying slightly less than the second couple's high bid.
'We wrongly assumed property prices would stagnate or go down'
Jenny Scott, a 43-year-old freelance event director, is looking to upsize her property in The Chilterns.
Her family is currently in a "semi-detached with limited potential" and are keen to move to a larger house with an extra bedroom and some office space.
She says her family of five put their house on the market a year ago, but took it off due to worries about finances when the pandemic hit.
"We wrongly assumed property prices would stagnate or go down," she says.
They have now had an offer on their house for roughly the same price they accepted last year, but houses they're looking to buy have had a price increase of £50,000 to £80,000.
She says: "There's massive pressure I think on people suddenly wanting to upsize, they want the bigger detached house and of course there's just not as many of those and there's massive demand for them.
"There's a lot of people moving up from London, they're desperate to relocate and be here by September so they get the stamp duty reduction and also get their children into schools - our buyers are looking to do exactly that."