Casper, if you have sale agreed on your own house then you will expect to close soon? You could try to put a clause in contract whereby the house you are selling is used as security against the purchase of new house. The key thing for the seller though is that you convince them that you are in a position to close the purchase of their house very quickly i.e. formalise and sign contracts, deeds of transfer in one step, and be ready to hand over the full amount (loan cheque) owed to them.
However, as another poster has written - this is sellers discretion, they may not want to take this risk.
Your solicitor should be advising you on all of this.