Conservative councillor James Hockney, who represents Bush Hill Park in the borough of Enfield, and who started the petition three years ago, said many drivers are “using the road as a race track”.
TfL said it had “no immediate plans” to install the cameras, but that the road remained “a priority” for police monitoring.
In 2020, TfL installed cameras along the A10 between the M25 and Southbury Road.
But Mr Hockney said the same treatment was needed on the section south of Southbury Road, down to the North Circular.
“Sadly we have seen far too many serious accidents on the A10 - and we will not rest until we have all the Enfield/Edmonton A10 corridor covered with average speed cameras,” he told the Standard.
“If the Mayor of London thinks by placing average speed cameras on half the stretch, that it is job done, he is mistaken - and I urge him to listen and think again.”
The councillor hopes that by submitting his petition this week, it will be considered by the London Assembly at their next full meeting on September 7. The Assembly then votes on whether to formally pass petitions on to the mayor and other bodies like TfL.
A TfL spokeswoman said: “We know speeding is a major concern for people in the area and we installed an average speed system on the A10 in March 2020, which is in addition to the spot speed cameras being used to tackle speeding in the area.
"Although we have no immediate plans to install a fixed safety camera system between Southbury Road and Great Cambridge Road roundabout, the A10 corridor is a priority for the jointly funded TfL/Met Police Roads and Transport Policing Command, which continues to be deployed to the area to deal with a range of criminal and antisocial driving offences.
“Breaking the speed limit is illegal and dangerous and we will continue working with the borough and police to ensure that roads are safe for everyone who lives and works in Enfield.”
Mr Hockney said car noise was also a serious problem in the area, caused by the flooring of throttles, which creates a popping backfiring effect.
The issue was raised by Tory mayoral candidate Susan Hall in a written question to Mr Khan last month.
She said local people were “plagued by the noise of high performance or altered exhaust cars” and asked when TfL would install noise cameras along the busy road. Mr Khan’s team has not responded to her.
In answer however to a similar question from Joanne McCartney - Enfield’s Labour London Assembly Member - Mr Khan said: “While TfL continues to focus on road danger reduction and working with the Metropolitan Police to tackle the leading causes of this, its strategy to combat noise pollution is to focus on encouraging walking and cycling and reducing motor traffic volumes.”
He said that while Government trials had been taking place on the use of noise cameras in other parts of England and Wales, TfL had no plans at that time to participate.
In December 2021, City Hall said that the installation of the cameras in March 2020, the police had dealt with 47,282 speeding offences on the A10.