The extension of 20mph zones to cover most of the borough is one of the measures that Southwark Council is currently consulting on following the publication of the draft Road Safety Plan.
The proposal doesn't affect main roads controlled by Transport for London.
Cllr Richard Thomas, Southwark's executive member for environment and transport, said: "We're committed to ensuring that Southwark's roads are made as safe as possible by tackling excessive speed and the irresponsible use of cars which are the main sources of danger.
"The real and perceived dangers of roads keep children indoors, stop people from walking or cycling to their destinations, and restrict the movement of people with disabilities.
"The benefits of lower speeds in road safety terms are clear; research shows that when hit by a vehicle at 40mph, nine in ten children are killed. Hit by a vehicle at 20mph nine in ten will survive.
"We need the community and partner agencies to give us their views on the plan if we are to deal with the sources of danger on our roads effectively."
Short presentations on the plan will be delivered at each community council meeting throughout September and October, and copies of it can be downloaded from the council website.
Last week the Corporation of London agreed to think again about creating a 20mph zone as bicycling barrister Ralph Smyth was about to launch a High Court action to force it to take action.
Mr Smyth's application for judicial review on behalf of the campaign group City Cyclists was withdrawn after Mr Justice Collins, sitting at the High Court, was told an agreement had been reached and the matter was to be reconsidered.
City Cyclists pointed to the much-publicised death of Vicki McCreery on Blackfriars Bridge back in May and said they hoped introducing a 20mph zone in the Square Mile could lead to other parts of the capital, such as Covent Garden and Oxford Street, also introducing similar speed limits.
Campaigners highlight the fact that 20mph zones are appearing in residential areas all over London, but not in the centre, where more people walk and cycle and where safety problems are at their worst.