The government has urged people not to move house to try to limit the spread of coronavirus across the UK.
Buyers and renters should delay moving while emergency stay-at-home measures are in place, it said.
Its comments come amid reports banks are pressing for a full suspension of the UK housing market.
Lenders are concerned about the effect of the pandemic on valuations, according to the Financial Times.
Banks are also worried about granting mortgages during this period of extreme economic uncertainty, the FT said.
The government said that while there "is no need to pull out of transactions", "we all need to ensure we are following guidance to stay at home and away from others at all times".
If a property is vacant, people can continue with the transaction, although they must ensure they are following guidelines with regards to home removals.
But if the house is occupied "we encourage all parties to do all they can to amicably agree alternative dates to move".
Property listings websites say that interest in moving home has slumped amid the coronavirus outbreak.
Zoopla said demand in the week to 22 March fell 40% from the week before and it predicts housing transactions will drop by up to 60% over the next three months.
Meanwhile, an increasing number of sales that had been agreed before the lockdown are falling through.
The property listings site said the UK housing market had a strong start to the year before the coronavirus outbreak crushed demand.
The pandemic has led to a "rapidly increasing" proportion of sales falling through, as would-be buyers "reassess whether to make a big financial decision in these shifting times".
Rival Rightmove also said the slowdown in the UK housing market had been "significant".
"The number of property transactions failing to complete in recent days and likely changes in tenant behaviour following the announcement of the renters' protections by the government may put further pressure on estate and lettings agents," it said, referring to the recent ban on evictions.
In response to the crisis, UK Finance, which was formerly known as the British Bankers' Association, said lenders would extend mortgage offers for people who were due to move house during the lockdown.
"Current social distancing measures mean many house moves will need to be delayed," UK Finance chief executive Stephen Jones.
"Where people have already exchanged contracts for house purchases and set dates for completion this is likely to be particularly stressful," he said.
"To support these customers at this time, all mortgage lenders are working to find ways to enable customers who have exchanged contracts to extend their mortgage offer for up to three months to enable them to move at a later date."