I'm in the US so you will have to make conversions. A person to stay in the house would have to be bonded. They are different than sitters. If you truly want the best help you want at least a nurse.(LVN at the least in the US, depending on their pay...some make as much as $17 an hour) Considering that under private pay here they have to carry their own benefits here an LVN to live in is close to $65,000 a year. That is giving them their own room and 2 days off. Still well above the average pay for the system here. But then you are also holding them accountable.
Still if you are looking for an easier way than a home you may think of moving in yourself or moving them to you then having a person trained to sit with your AD patient. Unless you are very well off it is going to be expensive and it can be quite time consuming. I hope someone can better answer your question for where you are, otherwise all I can do is offer advice on how to make it a little easier and albeit a little cheaper.
I looked at this a couple of years ago - an agency worker in Lincolnshire would cost between £12-£15 an hour. However, I do know someone who had to have round the clock care (non nursing) and employed their own staff and were paying them £9 an hour. This was also Lincolnshire. I think if you do this you need a minimum of 3 people in order to provide round the clock coverage and allow them to have time off. I also think the standard way of arranging it is 2 weeks on 1 week off with 1 person as a "floater" to pick up the slack. The Lady always used to be a place to advertise for this sort of help, but I'm a bit out of touch now.
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.