I managed to negotiate a new mortgage deal, after much tribulation.
We're apparently in negative equity, so no mortgage provider will touch us with a bargepole.
But I was able to renew our deal with our existing provider, as we didn't need to go through any new evaluations or anything like that. By paying an extra £50.00 per month and with a lower interest rate we've shortened the length of our mortgage by 5 years, to 15 years. Go us!