Motor traffic will be banned from the short section of Bermondsey Street between White's Grounds in the north (by The Garrison pub) and the Tanner Street junction in the south.
The restriction on motor traffic means that cyclists crossing Bermondsey Street from Leathermarket Street to Tanner Street on Quietway 14 will no longer have to contend with cars at the junction.
The partial road closure could be introduced in August or September this year.
The council wants to turn off the traffic lights at the Bermondsey Street / Crucifix Lane / St Thomas Street intersection and convert it to a raised junction with 'give way' signs on a trial basis.
There are also plans for a cycle contraflow on the eastern end of Snowsfields.
The proposals are part of Southwark's Streetspace Plan which will be approved by the borough's cabinet next week.
"Southwark's Streetspace Plan sets out its overarching aspiration to maintain 50 per cent less driving than before the lockdown and to accelerate a modal shift towards active travel to retain as many transport, health and environmental benefits as possible from the lockdown," said Cllr Richard Livingstone, cabinet member for environment, transport and the climate emergency.
He added: "COVID-19 and the lockdown have shown that traffic can be significantly reduced and the benefits of cleaner, quieter and safer streets and neighbourhoods.
"We already knew before the pandemic that we need to improve air quality to tackle the respiratory health of vulnerable people and communities who have experienced greater impacts from COVID-19 and the lockdown.
"If Southwark maintains lower amounts of driving, the borough will see a sustained and significant improvement in the environment and many people's quality of life."
Southwark Council asked Transport for London for £50,000 to implement the measures on Bermondsey Street but has only been allocated £10,000. The council says that it is in discussions with the Team London Bridge business improvement district about funding to to help make up the shortfall.
Local group BermondseyStreet.London and London Bridge & West Bermondsey councillor Damian O'Brien have been involved in the behind-the-scenes work to get the proposal to this stage.
Last week the council suspended a number of loading bays on Bermondsey Street and erected temporary barriers to widen pavements for social distancing.
Bermondsey Street had also been touted as a potential candidate for timed road closures in a report on air quality by Southwark's cross-party Environment Scrutiny Commission.
The scrutiny report, to be considered by cabinet next week, also names St Thomas Street and Elephant Road as streets where motor vehicle access could be limited at certain times of day.
Southwark's Streetspace Plan is intended to complement the Mayor of London's Streetspace initiative to provide short-term benefits for pedestrians and cyclists in the age of social distancing, as well promoting a longer-term shift away from the dominance of motor vehicles.