There was a piece in last Saturday's property section of the Telegraph about exactly this sort of thing.
However, it was talking specifically about countryside homes so may not be directly relevant to your situation. Here are some extracts:-
Warning over countryside house price bubble
Urban exodus buyers may find they have vastly overpaid in the frenzy.
[...]
[An estate agent] said prices in rural areas within 90 minutes of London, such as the Cotswolds, south Oxfordshire and Hampshire, are up 20pc year on year.
[Another estate agent] said "A lot of people have bought houses in B-grade locations and have paid A plus prices. They are going to be told their properties are worth considerably less than they paid for it".
"A lot of buyers are shooting from the hip and making massive compromises. There are plenty of people who are buying now, making a medium term move, who could find it quite expensive when they come to sell".
[...]
Part of these soaring prices was due to a dearth of homes on the market. But now, supply is starting to rise. Savills estate agents said that newly vaccinated older downsizers, so called "second-jab sellers", are preparing to bring properties to market.
"I'm getting more calls from the older generation who weren't so keen to have people coming around in lockdown. Now they're feeling safer."
The next few months will be competitive for buyers, but these vaccinated downsizers will start to bring their homes to market just as demand starts to soften. The return to the office means many Londoners are pausing plans to move out to the country.
"We are already noticing buyers who have gone on hold. Country property is now very expensive, they're doing the calculations and they're thinking actually they can't afford it."
He added: "Others are questioning if they will be doing flexible working as much as they thought they would. Maybe they don't want to be the person in the office who has a two hour commute when the rest of the team is in the capital.
"People are thinking: hold on, do I really want to move out of London?"
But demand will continue to outweigh supply for the next 12 to 18 months and that will underpin prices.
[...]
Strutt & Parker's Ipswich office has already exceeded last year's total income in the first three months of 2021. Demand is also high in Norfolk, Dorset, Somerset, the Kent coast and the Cotswolds, he said.
The above is just some extracts from the longer article.
It's mostly talking about countryside property (naice little villages etc) so that may not be directly relevant.
However, one thing that I think will apply more generally, is older people feeling safer about putting their homes up for sale (regardless of where they live) as they will have had both vaccinations by now and so supply will start to increase.
But how long that will take is anybody's guess.