TipTop is the only one I can think of in the Solent area but they don't deal directly with the great british unwashed. Instead they trade through a country wide network of chandler and sail maker "partners".
Chances are if you take a sail to sail maker or a chandler advertising sail laundering that's where it'll go
I went along there once as there was a stain on the sail that wasn't there when I sent it off via the sailmaker and it was the only way to get it back to be re-cleaned in time for me to set off the next week.
At that time they used a pressure washer, some sort of detergent and a bloke with a broom rather than a scrubbing brush.
But almost everyone who offers sail cleaning uses them. For what it's worth I've used a sailmaker as they can then check the sails over and do any necessary repairs.