Well, at least you won't hit much traffic!
We're not in the UK now so I'm not sure what the weather is like, but if it's 'behaving', the early arrival could actually be great. I love London in the early hours before the streets are crowded, etc..
Victoria Station is a great location at which to arrive. If you felt like walking, you could easily make your way over to Westminster Abbey and Parliment, Big Ben, the Eye, etc.. If it's not windy, just walking along the Thames is such a nice thing to do, walk across the bridges, take pictures. You could even as easily walk to Buckingham Palace which is right in front of the absolutely beautiful St. James' Park (love it!) and follow that to the Horseguards Parade and then either left to Trafalgar Square or right to Parliment...or straight across to, again, the Thames. Really, if the weather is decent, there are stunning views all around you there. One of the best maps of London is available at the Tube stations...just ask the person behind the ticket window for a BUS MAP for London; we found it to be by far one of the best maps available (free).
You can also check out the big bus tours of London; you can hop on and off all day. Can't remember how much they are. If you decided to do this, the company with the maroon and tan buses are the ones that have a live audio tour and are very good. Not sure that you want to do this tour closer to rush hour though; not fun.
There is also the public bus that leaves from Victoria...I THINK it's Bus 9 and I think it leaves right from Victoria but maybe just outside...and hits a lot of the sites on it's route. It stops at all the bus stops though so keep that in mind if you're not patient and just want to get to where you're going. 13 takes you up near Abbey Road if you're into that. 24 will take you up through Trafalgar Sq, funky Camden, and to the Heath (Hampstead) if you're wanting a little variety. If you're going to do this and/or ride the tube, you should purchase some sort (not sure how long you'll be in town for) of Oyster card to benefit from the high discounted rate.
You can also take a boat down/up the Thames; from Westminster, you can head east on the Thames and go under all of the bridges and what not. See the sites from there.
The London Eye is really nice; not sure what time it opens, but if you're there early enough, you won't be standing in any queues I'd imagine. Covent Garden is really fun -- and if the markets open, you might find some things you'd like to take home with you.
On yet another side of Victoria, Hyde Park is fantastic too, and Royal Albert Hall is beautiful --- not sure if you can get inside, but gorgeous outside too.
There are tons of cafes/coffee shops around. And as LC mentioned, the museums are free, so if they're open early, it's an option.
Overall, if you love photographing, London is an AMAZING place for pictures with all of the beautiful architecture and just all around interesting views. Enjoy!
