I hope the banks don't do that, I'm still in the process of purchasing!
In response to your question, they're certainly not going down where I am (London). My offer was accepted in early July, and is currently going through legals. I've been keeping a close eye on the market (i.e. refreshing Rightmove every couple of hours for the best part of 18 months).
Prices were static throughout the first lockdown, given nobody could do anything much, so only those who really had to move did. Following lockdown, I observed an uplift of a few percent, right until the start of this year. Then things went crazy in January, and have stayed pretty evenly up there until the June stamp duty holiday ended.
"My house" went on the market in mid June, so the vendor wasn't looking at capitalising on the stamp duty savings. The price has been locked in for 14 weeks and counting. Of the few houses coming on since, all the 3 bedroom houses I have seen are priced at between £25-£100k more than mine, despite mine being in good condition and in a great location. If my vendor put it back on the market, I've no doubt they could easily get £50k more (not from me as I'm already at the top of my budget).
The issue really is supply, especially in London, and particularly if you are looking for a 3 bedroom house. There are so many buyers and so few sellers that unless interest rates rise significantly (and by that I mean a couple of per cent, which is extremely unlikely to happen in the period of 6-12 months starting tomorrow), demand will likely hold firm, resulting in the high prices being here to stay. I'm clinging on to my purchase as if it falls through I won't be able to afford anything else for a year while I build up more savings.