We went to Simurgh Persian Restaurant on New Year's Eve because they were having a bellydancer at 8. We reserved for 7:30 and asked the waitress when the dancer was dancing. She said, 9:30. We were there until 10, but we didn't see any bellydancer arrive. That was rather disappointing and unprofessional on the dancer's part.
Afterwards, we went to Trafalgar Square. If you read any of the London websites regarding NYE celebration, you'll read that there is no organized NYE event at Trafalgar Square. However, for many years, thousands of people have gathered in the square similar to Times Square in New York City. There were even a jumbotron, fountains and statues blocked off, and loud speakers. We were able to catch the 1 million pound fireworks show at the London Eye on TV. I've seen my share of fireworks shows, and this one was definitely one of the top.
Here is the photoalbum for Nov and Dec 2003 in London:
http://lily.rupture.net/pics/London2003NovDec/