I’m in London and know of 2 from hairtell but I want to put a few more on my list.
Are you seeking electrolysis or laser clinics?
Alma Soprano XLI is the best laser out there.
It tells you where the nearst providers are to your zip
Take a look at the sticky posts. There are links for provider searches. Some are specifically for the UK. Laser manufacturers also have provider locators on their websites.
There are also many London threads on this forum and there are definitely more than 2 clinics mentioned there.