If I shook hands with a prospective seller and signed a contract to purchase a house for a set price and prior to the closing the market conditions had reduced the market value of similar houses would we then be permitted to renegotiate the price or is it subject to mee sheporah? Thanks.
There are several issues here.
Firstly, Mee Sheporah is relevant only if money was paid for a sale but no other kinyan was effected. This is not the case in your circumstance.
The relevant question is whether the contract that you signed prevents you from reneging or not. It is unclear from your question what kind of contract was signed. If it was a deed of sale, usually neither side can back out unilaterally.
Sometimes, however, the parties sign a contract which is nothing more than a declaration of intent to conclude a sale. Whether either side can renege or renegotiate will depend on the text of this contract.
Even if no contract at all was signed but a definite commitment was agreed by both sides, the Halachah does not consider it acceptable to renege on such an agreement (unless unforseen circumstances arise) although one who does renege can not be forced to continue with the agreement. If the price changes significantly, there is a difference of opinion among the Poskim whether one may renege on the agreement, and their are opinions that permit it (although it is commendable to stick to your word).
However, one may always request that the seller bear in mind the drop in price and ask for a renegotiation of the price, but one cannot demand it.