I just had a look at cycle.travel. The route it suggests is more or less the way I would go, except for the bit via Cudham (same road as used on the Shark 200 and Greenwich Mean Climb 300), which is admittedly much nicer than the A21 but the climb to Cudham is viciously steep. Instead, bear right in Downe to go past Charles Darwin's house and continue southwards to join the A233 south of Biggin Hill, then turn left onto Pilgrims Way - slightly longer way round but skirts around the valley.
A bit further on, you get to enjoy the descent of Hubbards Hill, or you could turn left onto Gracious Lane and go via the seriously fast descent of River Hill instead - it's a big main road but wide.
The first bit of the route out of Central London depends exactly where you're starting and whether you prefer fast main routes or back streets.