Street to motor vehicles at all times, improving on the current temporary arrangement with materials that fit with the character of the area," says Southwark Counciol.
"This change is in line with guidance from the emergency services on how to best protect those visiting the market and surrounding businesses."
Stoney Street was one of the scenes of the 2007 London Bridge terrorist attack.
The council adds: "Closing Stoney Street to motor vehicles at all times, plus developments in the area, could potentially increase the amount of vehicles using Bedale Street; therefore, we propose to install traffic calming measures such as raised pedestrian crossing points and additional loading restrictions on Bedale Street to improve safety for those using the market and walking through the area."
Further details are on the council's consultation website where a survey can be completed until Wednesday 9 November.
• An online public meeting is scheduled for Wednesday 26 October.