The best was the Langham that had "broadband" access that was in fact slower than any dial-up I had ever used. For 14.99 GBP per night IIRC.
Then again these hotels and their management are so out of touch with reality it is ridiculous. A friend of a friend who is the manager of a serious London hotel told me that he needed to use an "approved" supplier for wifi and to put it in the lobby cost 25,000 quid (done 6 months ago). This is nuts.