Today I received my DTV from the Thai Embassy in London, in about 5 working days from account creation to visa.
At first I had applied for a private cooking course with a professional chef, however I changed my strategy to Muay Thai lessons after being requested by the London embassy specifically for a headed confirmation letter from a school.
I confirmed with the London embassy that yes, when applying from the UK I must be applying to a school, not with an individual. This is slightly stricter than the official "Thai department of consular affairs (Bangkok)" line, who stated that it does not have to be a school and private lessons would be okay.
My wonderful girlfriend helped me find [members only] Muay Thai school.
They answered promptly to my initial email and booked me onto a course with just email correspondence which was great.
Bashir from Tiger Eye was very very helpful dealing with my request and seemed to have all the documents templates ready to go, which shows that there are schools actively participating in the DTV scheme.
Note on contacting the London Embassy:
Google reviews have stated that staff at the London Embassy of Thailand are near impossible to reach. This was not my experience. I called at around 4:30pm last Wednesday. I just waited past the dial tone, and the message that "[they were] only open until 12", reaching a member of staff in about half an hour.