I too am a very new london commuter and haven't ridden a bike since my paper round circa 1992.
I've done the Streatham to Waterloo run about 20 times so far.
My learnings to date are:-
Find a route on quieter roads while you get used to it, the A23 by Streatham Ice Rink to Streatham Hill is effing scary so I've worked out a route via Clapham north.
Bus lanes are your friend
Practise cycling in a car park or something, looking behind you shouldn't result in veering into traffic.
Get a decent lock, and leave it at work, get a smaller one for buying your shopping on the way homw
Don't play with the bigger boys. People do crazy things on bikes, don't follow them.
Be VVV careful jumping red lights, in 20 attempts I've seen a couple of people come unstuck.
If you can't pull out to change lane because of traffic, don't stress, just get off and cross the road as a ped!