I have worked as a live in Carer when I was younger. This was done via a large national Care agency, who also provided qualified Nurses if required. It is very rare that the Care is delivered by just one Carer, a shift pattern divided by two or three carers is more usual, its just too much to expect of a single individual without allowing them a regular period of 'Off Duty'!
There used to be a company by the name of 'Country Cousins' who provided a national live in care service where two carers worked a rota of a fortnight each, giving them time to have some family life of their own. The service is quite expensive though, and you are also required to provide Food for the 'Cousin', and re-emburse them for their travel costs to and from their home Address every time they they had their fortnight off.
Quite a large amount of their Clients were London area based. The Cousins came from all walks of life, and all age groups and Nationalitys. Many of them were retired themselves.