We visited London in June 2007 on a Scandinavia-Russia pre-cruise.  Staying at the City Inn, Westminster, we were able to walk to a number of places and avoid taxis.  Big Ben,  Parliament and the river cruise dock were a short 15 - 20 minute walk over mostly level sidewalks. 

The City Inn is a great hotel.  If your room is not ready when you arrive, they will store your luggage while you have breakfast or begin your London sightseeing. Our room was adequate, even with all the bags we had for a 14 day cruise.  The bath was small but very clean.  The view was not special but we did not intend to stay in the room very much so it did not matter.  The hotel restaurant was extremely pricey, in our opinion. An English Breakfast was approximately $34 or 17 GBP.  Soft drinks were $5, bourbon $10, etc.  The concierge was very helpful and pointed us to two restaurants that were great.  The group wanted to experience a real English pub and the White Swan Pub was all of that.  The food was delicious and the atmosphere was what you would expect and the cost for the meal a drinks was only $43.  This was also a short 10 minute walk from the hotel.  The other restaurant we visited twice was Gran Paradiso, a small Italian place with excellent food and service.   The first night we only had two couples but the second night we had a group of 16.  The owner/manager set up a private room upstairs, complete with his live orchids and Italian music.  Again, the food was great.  We would highly recommend both of these restaurants.