I have been to London a few times at New Years, and it is a good atmosphere, in order to make the most of it you need to be organised.
If you go to Trafalgar Square, you have to get there early, as you won't get anywhere near if you turn up at 23:45. When I was there, there were some LED sign's, and at 00:05, they then started flashing, 'Met Police wish you a Happy New Year, now go home'. You're not encouraged to hang around!!!
Last year I tried to get to the South Bank. From here you have a good view of the fireworks which are over the Thames. We got distracted by the pubs on the way, and got there to late. The police had closed the roads down to the south bank, and as a consequence we didn't make it to the South Bank. We ended up on Millbank, and had to watch the fireworks through gaps in the buildings.
I would recommend that the South Bank is a better option than Trafalgar Square. But you will probably have to get down there 2/3 hours early before the police start blocking the roads.
Take a bottle of champagne, as everyone else has one, and if you don't have one, you feel left out!! Take some party poppers, see above.
If you want to make the most of New Years, I would have something organised for after midnight. You will need tickets for clubs, and you might want to check out some pubs. After midnight, you're encouraged to disperse, so you probably want to move on elsewhere.
You said you had some accomodation booked, but, last year we booked some accomodation at 11:00 on New Years Eve. We used laterooms.com and there was loads of availability. We stayed in Pimlico for about �50, and everywhere is walking distance from there.