First of all, have the hospital stated that they will be carrying out a continuing care assessment? If not, ask them if they intend to do so, it is something they have to do. If they try and say it is not required insist on it.
Secondly, a new national framework for assessing eligibility for continuing care comes in to effect on the 1st October and it replaces all the others that have been used by Primary Care Trusts and Strategic Health Authorities up to now. It means there is one criteria instead of the 28 that were previously in existence, but it is new and untested and I have no doubt the PCT's will have their own spin on it.
Yes, it will be a hard battle but there are plenty out there who are fighting it and will give you support. I don't know if you have found this site yet but there is lots of info on it which will assist you:-
NHS funded Continuing Care and the Coughlan case
Don't let them fob you off with lies, challenge everything and accept nothing until you have been able to verify the information they give you. They will do their damndest to convince you it is a social care issue and not health care, but stick to your guns.
PS What type of home have they said your relative will have to go into?