You can get free cycling maps from tube stations which are pretty decent and will help you work out where you are when you get lost. If you plan on doing a lot of cycling then buy a mini a-z from a newsagent. There aren't many weird road laws, but you'll probably find that riding is a bit different from NY (no grid system, slower traffic, narrow lanes etc). Like Pip said, make sure you don't go up the inside (left) of buses and lorries. Split the lane instead.

There should be a couple of people around next week for a drink and a ride one evenng. I'll see what I can sort out and let you know.