I live near Biggin Hill and so can give you some feedback on the area. It is a bit of a mission to get into Central London. You would need to get 320 bus to Bromley South station (takes about 25 minutes), and then get a train from there to London, which would take about 40 minutes. The bus is £1 single and the train would be about £4 return or £5.40 for a travelcard.