I used that cycle streets link above to find a quiet route to work and its pretty much all residential streets until London Bridge. I guess those streets have their own challenges with cars parked down both sides and not much room in between but it definitely looks less frightening than the tfl suggestion.

Ordered my ride2work voucher, should get my bike this weekend! Think I'll start with Dulwich Park until I do the council course. I noticed they do a group course over 5 sessions culminating in a Saturday ride to London Bridge which sounds good. Also if you're not sure they will lend you a bike for a month for a very small fee so you can try it out before investing.