'Afternoon Tea' is what I'm sure you're referring to. Check out http://www.afternoontea.co.uk/uk/london/, and you can refine your search with Gluten Free, of which 81 places are listed. Without tea, cakes, scones, clotted cream, strawberry jam, small sandwiches, etc. it's not an 'Afternoon Tea'. You might see 'Cream Tea' which is more or less the same thing, less grand and generally with only the scones, cream and jam, but it varies.
Hard to say a 'good' one, I'd imagine more or less all of them are nice, not too many crooks in the cream tea business, but of course, the lesser ones might serve pre-made scones warmed up, as opposed to home made scones.
My wife had Afternoon Tea at the 5 star Park Lane Hotel on Piccadilly, in the Palm Court and she said it was wonderful and cost around £33 per person. http://www.palmcourtlondon.co.uk/. I think you need to book online, not just turn up.
Most expensive ones I've seen are The Ritz or The Dorchester at around £50 per person, but that may have changed. You can also have a glass of Champagne added for around £10 per person more. These hotels are the top, top ones in London so actually the price didn't seem unreasonable to me. Very grand surroundings.
Picking any 5 star hotel in and around Piccadilly and I'd say you'll be in for a wonderful experience, something very traditionally English, even though most of us have never done it, lol.
I'd call and ask the venue that you choose which aspects of the Afternoon Tea are Gluten Free, just to be sure. I'd assume all of it, but you never know.
It's not something I'd personally try to do 'on the cheap' although M&S in Westfield, White City, do a very nice Cream Tea for about £5 per person.