That question was never raised when I engaged a care agency. I rang the agency, the care director went to meet and assess my mother. She did not specifically ask for my mother's 'permission' but my mother didn't outright object and it all went ahead. I don't think my mother had much idea what was happening - I never used the word carer, I just said a nice lady would help her with things she found hard to do like carrying shopping.
I have financial LPA, but not health & welfare, but that has not so far mattered in any of my dealings with the agency, or (latterly) with the care home.
