We get sitting service through Age UK. No waiting list where we live in East London and it's free but after the initial six weeks Social Services took over. It's integrated in the support plan now, together with day care.
If you indicated what part of the country you're in then you may get some recommendations and finding someone that way, personally recommended would be my preferred way of finding a sitter. You could google it putting your area in the search, I found several possibilities near me quite quickly or contact your local social services who may well have a list. There are voluntary organisations and asking at your GP's surgery are also possibles.