If by "signing over" your flat you mean "selling", then yes that is the best thing to do. Even if you have to take a few thousand loss on the sale, it is better to do that than to be repossessed or to hand in the keys. You can often force the lender to let you sell at a loss on the proviso that you will pay the lender the difference. You may need to go to court to achieve this.(posted 7837 days ago)There is no way of merely signing over the responsibility of paying your mortage though.
Your next stop should be the Do's and Don'ts list in the "Repossession" section of this site.