Cost of private care will differ by area. I looked into this for my sister in law, late last year, and the costs were a minimum of £700 a week. Then there are additional expenses if the carer were to attend appointments, use of car etc etc.This is on top of domestic running costs for the home.
She now resides in full time residential care, paying full costs of £387 a week. There are additional costs, but these are minimal and varied...hair dresser, chiropady, days out.
You need to get an information pack from your local social services, this should supply contacts offering different services. On e more thing, if you were to go through social services for HOME CARE, you may not get the full help you need, due to staff limitations.
Hope this helps.