Dear op, the following comments assume you are buying a family home by mortgage - and not an investor with cash needing a return. If your loaded, or trying to use residential property as a way to cash in - then I hope you get burned.
Put all the "Its a shitty thing to do" comments to one side. It's happening a lot at the moment for good reason.
Buying a property is a massive financial decision for you and your family. You need to do what's best for you and yours. End of. Treat it as the life changing financial commitment that it is.
You do not owe others involved in your purchase anything, they are strangers. They are looking out for their own interests - as must you.
You need to decide, without delay, wether or not you are paying a price for the property that you are comfortable with. Factoring in to that the fact that the property may, or may not reduce in value. Interest rates may go higher, may stay the same or may reduce ? No one has a crystal ball, the majority opinion seems to be that values have further to fall if the status quo remains. I agree with that but have no idea how significant a correction this will turn out to be.
My advice is if your thinking the property might be a short term solution- and that you would probably be moving again in the next few years - then you need to be very afraid of overpaying.
If this property is going to suit you for a long time then you are historically unlikely to loose out. The fact that it was a bit more than you wanted to pay really won't matter.
On the subject of how best to achieve a reduction. If you haven't already, then you need to pay to have a full structural survey done that includes a market valuation. It will almost certainly find issues that you can use to renegotiate. It will almost certainly value the property lower than the estate agent, vendor or mortgage provider has done.
You need solid reasons to renegotiate successfully, pay a little to get them. If it turns out everything is hunky dory with both the structure and the valuation then it's also money well spent for the piece of mind of KNOWING you didn't overpay at the time of purchase.
If your research leads you to believe, as some do, that a large correction in values is imminent - better you just pull out and wait.
Good luck