Me and my mum shifted my dad without permission or blessing or anything. Social services were not involved - they didn't really care. He'd been assessed by the new home during yet another hospital stay and we shifted him with a mobility taxi.
The home he's in has zero say in this. Covid throws a spanner in the works, and there's an argument there must be a place ready for him, but I reiterate, it's not a prison (unless he's sectioned).
Ring round other homes and ask to speak to a manager there, they'll have a more up to date idea on how things are working now and if they'd take him.