Don't do it ..................... for all your sakes.
With shorthold tenancies, you could be moving every six months............... not likely I know......... but it's always hanging over you. Concentrate on clearing the card debt first whatever it takes......... even by extending your mortgage. It'll be way cheaper as Brighty says, than paying the card companies.
Keep your house and look hard at ways of freeing up some space....... there's always something that can be done ................ good luck