Rightmove said that, until 23 March, the number of house sales being agreed was up 11 per cent since the start of the year, compared with the same period in 2019.
It was the best start to the year for four years, the company said.
When the lockdown was announced, visits to its website fell by around 40 per cent, but there have since been some slow signs of recovery, it added.
Social distancing measures to limit the spread of coronavirus mean people have had to put off their plans to move until a later date.
Lenders have been giving extensions on mortgage offers to help people who had been on the brink of moving. Rightmove said most sellers already on the market, and those with a sale already agreed, appear to be continuing with their plans to move once it has been deemed safe enough to do so.
Available stock for sale fell only marginally, by 2.6 per cent, and since the lockdown the level of sales falling through is similar to what the property website would normally expect to see.
Across Britain, the average asking price for the dwindling number of properties coming to market from 8 March to 11 April fell by 0.2 per cent month on month to £311,950.
The price of property coming to market had reached an all-time high of £312,625 in the previous month.
However, Rightmove said, given that the housing market cannot currently function as normal, the latest price figure is not meaningful.
With current difficulties in carrying out property valuations, and many people uncertain about the extent to which their incomes will eventually recover, some lenders have temporarily restricted the mortgage deals on offer.
Miles Shipside, Rightmove director and housing market analyst, said that, looking further ahead: “We need to avoid a repeat of the post-credit crunch mortgage famine which took from 2008 until the 2013 launch of Help to Buy to bring the mass market back into play with low-deposit mortgages.”
Rightmove said much will depend on future trends in employment rates.
It said some housing market activity needs to be kept “simmering”, and a post-lockdown plan must be put in place which can cope with maintaining social distancing during visits for marketing, viewing, valuing and surveying.