I'm sure they do. Same as with any form of broadcasting.
But it's not just in London. I have route I use quite often using back roads to Bognor on the south coast. FM is unusable for quite a chunk of that - DAB just fine.
My radio will switch from DAB to FM if the signal is bad. Obvious when this happens, due to the digital delay on DAB. And it doesn't happen often.
I would say DAB seems far more sensitive to the aerial used, though. Dunno why.