Is worse than in some "third world" countries I know. I was there the fatidic day of the opening of Heathrow's Terminal 5, but fortunately in another section of the airport so wasn't affected.
However, my Heathrow Express train from Paddington was delayed for almost an hour, as the thing just decided to stop dead in the beginning of the journey (but outside the station). Since I've already experienced quite a few problems in the tube during previous trips, I really wonder when (if ever) they will get their act together. I'm just amazed by the rivers of money flushed down the toilet because of downtime…