Another suggestion would be extending the Bakerloo line south from its current terminus as Elephant & Castle to Camberwell, they apparently looked at it in 1931 and again in 1947 with the plans having an intermediate stop at either Albany Road or Walworth Road respectively. It would only add another 2.5 or so kilometres to the network but it then leaves open the opportunity of extending it further by either taking the line southwards or eastwards at some point in the future.
IIRC they're currently seriously considering extending the Bakerloo line south to Camberwell and then turning east to Lewisham, potentially also taking over the Hayes Line from there to, not unsurprisingly, Hayes. One alternative I saw suggested on an amateur site was to extend the Bakerloo line south to Camberwell but then turn south-west to Brixton before heading south and curving east to Croydon. A new branch of the Northern line would instead turn off just after Kennington to go to Camberwell before extending eastwards to Lewisham and then taking over the Hayes Line to Bromley and potentially Hayes. The lines would be
They did a map of it
here. IIRC it was a number of years back so I don't know how that would play with regards to passenger numbers and travel patterns nowadays, they were apparently fairly knowledgeable about these things though from what I can remember. Some of our resident rail and transport experts can weigh in here. One thing I did like about it was that it would push out the tube to the areas south of the Thames that have so far been cut out of the system and instead had to rely more on surface transport or heavy rail lines, they also tie in nicely with other lines and the Overground and Docklands Light Railway. The Bakerloo extension would add about 15 kilometres and the Northern line one roughly 16 kilometres to the network, the costs however would obviously be rather large.