Alternativly take the 285 bus from Heathrow (Central Bus Station) to
Feltham Railway Station and catch the train to London Waterloo. Make
sure that you travel on a train that has come from Reading or Windsor,
and avoid the longer journey via Hounslow.

If travelling to the northern bit of Southwark, at Waterloo take the
Jubelee line east to London Bridge, Bermondsey or Canada Water, or the
Bakerloo line south to the Elephant.

If travelling to Peckham, Camberwell or Dulwich take a bus straight
from Waterloo.

Pay for all of this by buying a Zone 1-6 day travel card at Heathrow
Tube station.