If you can self fund I would start by looking at options. You might ask advice from people who know local provision eg the GP, Priest/vicar. Go and look at them and then get your parents to also look at them. My guess is that it will be crucial to have them on board.
Whilst looking ask lots of questions. I learnt a lot about options from care home managers.
One option might be to start with a couple of "respite" care. This then gives a chance to see if it suits, and even if not, gives your mum a rest.
It might also be an idea to ask for a Social Services assessment. This will give you an idea of what you need. Nursing care etc. SS also have a pretty good idea of what is available and you could ask them to suggest which homes you might look at. (They wont be able to make recommendations.)
Alternatively would extra-sheltered or similar, work. They both move, have their own flat but have the support of wardens, handymen, catering etc?
Others will know more than me. However you would presumably need Social Services to assess him and decide he needs residential care. If the issue is that his wife does not want carers in the house this might be difficult. His wife might also need to be willing to part fund either because his pension is such that Social Services expect it or because the preferred home is more expensive and requires top up.
You might phone both Social Services and Age UK anonymously to ask about what can be done and the financial contributions that your dads family might have to make.
nomoresleeps advice is spot on. A referral to SS will be your first move - you can self refer. There are nursing/ residential homes which don't require top ups but these are usually quite basic homes. You will be able to obtain a list of homes within the area from the social worker and view them. The Care Quality Commission inspect homes and give a grading so it is always worth reading their reports on specific homes. Another idea would be for him to be assessed by a Community Healthcare Co-ordinator to see if he is eligible for funding via the NHS, this will depend on his health issues. The social worker will also be able to advise on this too. Good luck it can be a mine field when you first start looking.
Ring SS and ask for them to do an assessment. My Mum is funded. You need to know whether he needs a care home or a nursing home. Also whether he can be funded for nursing care or just for care. On this web site you can search for homes in your locality. www.carehome.co.uk/
It gives you links to inspection reports, vacancies etc. Then you can ring round to see who has vacancies. Then visit them but do not make an appointment to do so. Just turn up at reasonable times. Age uk website has a good list of things you should look for.