You shouldn't be taking the council's word as Gospel, and frankly neither should your solicitor. The council's only role here is to hustle as much money out of people as they can. They have no duty of care to assert or safeguard your rights.
You'll need to get proper legal advice on the extent of your liability here, particularly on whether the property ceased to be your father's PPR immediately upon his admission to the nursing home in March 2011.
It rather beggars belief that this could be the case within so short a timeframe, particularly if his/your agreement with the nursing home was on an ad hoc or monthly basis, and assuming that the house wasn't immediately let out, or there was no other reason why at least in theory he couldn't have returned to the house to live even temporarily had his condition improved or stabilised or had the nursing home arrangement not worked out for whatever reason.
However, in order to be sure, you'll need to have this checked properly, taking into account the exact circumstances of the case. Good luck with it.