Another alternative is to hop on the bus to Ladywell and pick up a train to LB.

Unfortunately, Lewisham are currently implementing a road improvement scheme to Lewisham High Street which means that traffic stacks up Ladywell Road towards Brockely cemetery and it takes for ever to get through to the A21:

https://consultations.tfl.gov.uk/streets...l-road.pdf

PS Ladywell works due to continue until the beginning of December.