Agencies
There are numerous Live-in Care Agencies in the UK, ranging from small ones serving a localised area to ones that operate nationwide as part of a healthcare group: one or two are franchises.
When choosing an Agency, try to obtain up to date information from a relative or friend who has already worked through them and also look at their website. Without this first hand information, you should, perhaps, only consider Agencies with a Local Representative who can answer all your questions.
Police checks
Criminal record checks (Police checks), both in your home country and in the UK, are part of the documentation required before you can be accepted by a Care Agency. The Local Representative will probably ask you to complete the application for an enhanced CRB (UK Criminal Records Bureau) check so that it can be sent in advance of your travelling.