The document - circulated by members of Speed Awareness Group Ardsley (SAGA) - related to a busy dual carriageway on Doncaster Road.
However, measures called for by campaigners - including average speed checks as seen several miles away on the A635 - have been rejected.
According to the Department of Transport - which is responsible for installing cameras - the Ardsley stretch does not meet the ‘very strict’ criteria.
Coun James Higginbottom, cabinet spokesperson for environment and highways, said: “The council justify a considerable annual investment in road safety on the basis of reductions in collisions.
“This is focused towards addressing those sites most in need of intervention first.
“The dual carriageway section of Doncaster Road in question has had three injury collisions in the three-year period from January 1, 2019 to December 31, 2021.
“It doesn’t meet the very strict, pre-determined criteria for speed camera implementation, which has been set by the Department of Transport.
“As a result, we’re not be able to support this part of the request.
“The council has recently installed 20mph speed limit signs on Doncaster Road in the vicinity of Oakhill Primary School, and as part of this scheme we will be taking speed surveys on the road via the school entrance in both directions.
“Surveys show that over 90 per cent of the traffic is travelling below the 40mph speed limit, and the 20mph (outside the school) speed limit signs will continue to be monitored to measure their effectiveness.”
He added that a new active travel route along the stretch, which will include three pedestrian and cycle crossings, is due for completion by March 2023.
Sir Steve Houghton, leader of the council, asked if one of the crossings could be placed outside the school, but said it was ‘disappointing’ news.
He added: “If we don’t meet Department of Transport rules, we don’t meet the Department of Transport rules.
“There’s nothing we can do about that, but we’ll look at every other aspect.”
A statement from SAGA urged action given the danger posed by traffic, its speed and proximity to the school.
It said: “Residents of Stairfoot and Ardsley are requesting various actions to limit the excessive speeding of vehicles on the A635 dual carriageway between Stairfoot roundabout and Darfield.
“This is to protect parents, children, disabled people and the elderly and to give access to Oakhill Primary School and other amenities, whilst crossing the dual carriageway.
“These actions would contribute to the reduction of pollution caused by speeding vehicles.”