We didn't try any Chinese food last time we were there, but from what I've heard, London is probably not the greatest place to find authentic Chinese food (with or without good tea). I haven't been, but you could try Bar Shu
, a Sichuan place.
Usually the tea served in Chinese restaurants, whether in China or elsewhere, is not going to be high quality. Usually it's 'cha shui' (tea water, vs. tea) -- something warm, inoffensive, and not that strong, which is probably a good thing, since drinking much caffeine during your meal can make you lose some nutrients. I usually drink hot water instead.
Most Cantonese seafood / dim sum places will have set options for loose leaf tea (jasmine, ripe pu'er, chrysanthemum, pu'er and chrysanthemum mixed together, maybe a green tieguanyin, maybe some kind of roasted oolong), and often a small, per-person tea charge as well). These teas will be decent, but rarely excellent. Anywhere other than that, you're probably looking at cheap teabag tea, oolong or pu'er if you're lucky, but most often, scented jasmine. Even in the area where I live (in Los Angeles), which has thousands of Chinese restaurants, mostly catering to ethnic Chinese clientele, the tea is invariably from a teabag, except at the kinds of places mentioned earlier.
Maybe we have a different idea of what constitutes high end, but IMHO, kind a waste to have "high end" tea at a meal (before or after, maybe, but few restaurants have good facilities for that). Sometimes I'll get hot water and add my own tea, but here, you're looking for something that's "good enough" without being "too good", and something that will tolerate a range of temperatures, and long infusion times. Another thing I'll do sometime is take the spent leaves of tea that I brewed much stronger earlier in the day, and put them in the teapot at the restaurant. This is a good way to avoid waste, and since the tea has already been brewed several times, it won't get as over-extracted, and there isn't as much worry about the leaves not opening if the restaurant's water isn't hot enough..
Edit: Hadn't heard of Yauatcha - does sound interesting, and looks like they have a good tea list.