Some 44% of those in favour of a crackdown say officials should tell people to switch of their engines and fine them if they refuse, the RAC poll indicated.
Only a handful of councils use existing powers to hand out £20 fines, the motoring services firm said.
Two out of five (40%) of the 2,130 drivers questioned stated that they regularly witness vehicles parked at the side of roads with their engines running.
Some 26% have spotted drivers doing this outside schools.
More than half of those surveyed replied that they are more concerned about the impact that vehicle emissions have on the environment and public health than they were three years ago.
RAC head of roads policy Nicholas Lyes said: "Councils already have the powers to deal with this problem, but few are currently doing so.
"Many of the drivers we questioned would like to see some firm action taken against offenders. This is no doubt needed to bring about a change in behaviour.
"You could liken the current situation with engine idling to that of taking your own carrier bags to the supermarket: everyone knew it was the right thing to do, but few of us did it until a compulsory charge was introduced.
"While the law is already in place for idling, enforcement is limited if not non-existent."
In June, the Department for Transport announced it intends to launch a public consultation looking at increasing fines for idling drivers.
Local Government Association transport spokesman David Renard said: "Although fines to drivers who leave their engines idling are issued as a last resort, the legislation to enable this is hard to enforce in practice.
"Councils have prioritised changing behaviour by educating motorists, which is often more effective than issuing fines.
"As part of their review of air quality legislation, the Government should look again at whether these powers are working how they intended and whether they could be made simpler to use while still being fair to the motorist."