LT (LPTB?) had them many years ago - mostly for the "country area" routes using green buses, not the routes served by red buses. But I think, as a kid, I did see one in the north-west suburbs in the "red" area - maybe around Ruislip or somesuch. I'd imagine they'd still be needed in some areas on the fringes of London - or is it all done by local councils these days rater than by privatised bus companies?
There are still warnings in places in central London about low-hanging trees, so that bus drivers don't drive too close to the kerb. But these are cases where it's not just lack of lopping, but very old trees with a serious tilt, where the main trunk leans out over the road in a way that could conflict with the top deck of a bus.