Can you be a bit more specific about the type of house / region? There is bound to be someone here who knows the market in your area.
Alternatively, ask other agents and look at sold prices (although they are 6+ months out of date, so not completely accurate).
But I would suggest that prices have been rising, and will continue to do so for 2 main reasons - interest rates are going to keep falling (according to most experts) and there are increases to stamp duty in 2025, so people will be in a rush to buy before then - leading to an effective shortage of available properties.
Is £6k a significant percentage?
Do you want to give the buyer £6k?
Do you trust your agent?
He sounds dodgy to me, but if £6k is something you can swallow to put this to bed, is it worth it for your mental health?
Personally, I know I would feel aggrieved if I thought I had been conned, so would rather take my chances on a new sale - only you can decide if a bird in the hand is worth the possibility of cutting your nose off to spite your face 😉
Once you’ve decided if you want to continue with this buyer, this agent at £6k less, you can determine your next move…