My answer's probably too late for YammaY, but for anyone else in this situation with a relative in hospital, you have the right to insist that the social worker dealing with your loved one's discharge carries out an NHS Continuing Health Care Checklist.
This is carried out by the care worker, in consultation with the doctors and nursing staff, and with the occupational therapy or other staff who assess your loved one's mobility and their ability to look after themselves (or not, obviously), and you have the right to be in that meeting too and say your piece.
Depending on how your relative scores on this checklist, referral is made to NHS CHC locally, and they determine whether your relative's needs are complex enough that they need NHS Continuing Healthcare funding (usually a senior CHC staff member has to visit them in their own home after discharge to make an assessment).
This funding, if awarded, can cover fees for carers to look after them in their own home or your home, and would also cover fees that might be incurred later in your relative's dementia "journey" for nursing, accommodation and food if they need to go into a care home (in which case, discharge at that point can be effected straight from hospital to care home if they are back in hospital again).
This is NOT means-tested, so is independent of what your relative has in assets, and will solely focus on his/her needs. CHC can agree or disagree with your choice, but you can suggest the care home, and if you're lucky, they'll approve the one you choose.
My relative was incredibly lucky to find herself, at the end of this process, in a CQC-rated "Outstanding" nursing home solely for dementia sufferers, where she's loved and cared for in the way that all dementia patients should be. Fight your corner and latch onto anyone who seems sympathetic in this process. Good luck.