Has he had a full Local Authority assessment regarding his care needs? Even if you feel he needs a care home, the LA won't go down that route until they have ruled out other options. You don't say if your dad already has a care package . If not, an LA is very unlikely to consider a care home until carers have been tried. Also, it depends on what your dad wants. IF he had carers in to help with certain personal care tasks ( washing, dressing, cooking etc) that would support him to remain independent. If he does have a care package and it's no longer meeting his needs, ask for a reassessment . If it comes to the point where a care home is the best way of meeting your dads needs , and he agrees, then the social worker should bs able to tell you which local homes accept LA rates. Age Concern has quite a lot of good info on care homes etc.
Basically it comes to whether what your local authority will pay for care vs what the home charges. If you go and have a look round and chat to them, the manager will be able to tell you whether this happens.