Transport for London has launched a public consultation on plans to extend the Bakerloo line beyond Elephant & Castle.
TfL is asking for comments on a range of options for extending the tube via Old Kent Road or Camberwell and Peckham to Lewisham and possibly beyond to Beckenham and Hayes.
"An extension of the Bakerloo line is one of my top priorities and I have asked TfL to bring forward these plans at pace," said Mayor of London Boris Johnson.
"It would provide a vital new transport link for the people of south London and help to spur jobs, new homes and regeneration in this part of the capital. It has huge potential to breathe a new lease of life into a swathe of London's opportunity areas, as well as freeing up capacity on national rail lines.
"As London's population continues to rise it is essential that we expand the transport network in this way if we are to meet Londoners' needs and ensure our city's continued competitiveness and success."
Transport bosses put the cost of an extension as far as Hayes at between £2 billion and £3 billion.
Only a handful of completely new stations would be built, with most converted from existing National Rail stations.
Funding for new stations on the Old Kent Road would come from proposed housing developments in the 'opportunity area' for new homes recently designated by the Mayor of London.
It will be harder to find funds from developers if the Camberwell and Peckham route option is chosen.
"We welcome today's consultation on extending the Bakerloo line south of the Elephant & Castle," said Cllr Mark Williams, Southwark's cabinet member for regeneration, planning and transport.
"It's great that within a year we've gone from no-one believing this could happen, to the Mayor backing calls from Southwark Council for this extension.
"We fully support both routes – via the Old Kent Road, and Camberwell and Peckham – to significantly improve public transport in our borough.
"We will be working with TfL and campaigning for two extension routes as we believe both areas are currently under-served and need this additional investment.
"We are glad that more people are now joining our campaign and hope the Mayor gets fully on board."
Val Shawcross, London Assembly member for Lambeth and Southwark, said: "I very much welcome proposals to extend the Bakerloo line southwards, which addresses the south east London area's need for a transport infrastructure more in line with the rest of London.
"Both suggested routes in Southwark, if implemented, would address areas in need of high capacity transport and offer regeneration opportunities to communities who very much benefit from it.
"I urge everyone to look at the proposals and have their say on this exciting and overdue project.
"My only concern is that both of the routes shown through Southwark need transport investment and TfL should consider how to improve transport in whichever route option is ultimately dropped from the Bakerloo extension plans.
"What we need to see alongside this consultation is the Mayor of London bringing forward a funding plan not only to realise the vision of an extended Bakerloo line, but to deliver it far sooner than currently proposed as on its current timetable whichever route is chosen the Bakerloo line extension would not come into use until 2030."
The public consultation runs until Sunday 7 December.
Meanwhile Lewisham Labour Party has launched a petition in support of the project.