Thing is, the number of people willing to be live in carers is quite low. It can be a tough and isolating job, and doesn't work for people who have families of their own.
Then it's also very competitive to get a good live in carer. My DM started out by putting an ad in The Lady - but all her subsequent jobs came by word of mouth
I think your first sentence should read the number of qualified and good people willing to be live in carers is quite low. There are in fact lots of people willing to do it who are unqualified and desperate.
You have to be very careful if you are recruiting yourself because there are a sector of people who see it as a way to get free accomodation, no bills and food paid for. As you an imagine this sector is not people who have a lot of financial choice or see caring as a vocation.
I placed an advert and had lots of replies but lots of them were people who were unqualified. There were a lot of foreign nationals (especially from Nigeria it seemed - not joking!) with no experience and no evidence of a right to work - with African addresses and phone numbers who were looking for some kind of visa I think. There were people who lived abroad and funded their life by coming to the UK to live in care for a few months at a time. It was extraordinary really.
Many people I have spoken to have said they found good people by using agencies and when they found a good person making them an offer to hire them directly. So if an agency is charging £50 an hour and the poor worker is getting £10.42 an hour, if you say to the worker come and work for me for £15 an hour, its a win win except for the agency. most of them have penalties for hiring staff (stealing their employees as they see it) directly but lots of people do it on the hush hush. You do need to make sure the worker is insured though or if you are formally employing them that is all dealt with correctly.