Below is a picture of the possible route joining the Bakerloo line to existing lines that go through Peckham, Lewisham, Catford and on to Hayes. I have included the ELL Extensions phases 1 and 2 to show what the basis of a South East London tube system would look like. (Unfortunately I have a problem with the size of images.)
   

The only infrastructure work that would be required would be extending an unused underground tunnel from E&C to Camberwell and bringing it to the surface. Reopening Camberwell station would also make sense.

Camberwell train station (closed in 1916)


This Bakerloo line extension would interchange with DLR, Croydon tramlink, and ELLX phase 2 with a link to Clapham. An interchange with ELLX phase 1 (our line) could be provided at Brockley station.

My prediction is that we should not need to wait more than 50 years for this extension to be built.