I have cycled into the city for 2 1/2 years now. In contrast to a lot of people who prefer quieter routes, I actually find that the main roads are easier. You move with the traffic and Bus Lanes are also big Bike Lanes. There are less parked cars with doors flying open (red routes) and it's much quicker all round.

The easiest (shortest) route into the city is over Horniman, Lordship Lane, turn onto Barry Rd, Peckham Rye, cross the High St, along the old canal (no traffic) then up to the Old Kent Rd under the flyover and along to Borough Tube station, then turn right up Borough High St and over London Bridge.

I got bored with that and started going through Camberwell up to Vauxhall then over Westminster Bridge and along the Embankment. Adds 2-3 miles (about 10 mins) but great sightseeing on a nice day.

Aside from that if anyone needs convincing:

Saves train money. Burns fat. Free beer both in terms of cash and calorie offset. Do the maths.