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I think it price changes have been obvious since the end date for the stamp duty holiday was known.
The stories of a cooling market seem to be written by "everyone" that is prospective buyers, estate agents or clickbait merchants. So personally I think it's bs.
All the local solicitors haven't been taking any new clients for about two months. That can't be helping the movement of market, I don't think that means price falls though.
Presumably if everyone thinks the market is going to do something, its probably already priced in.