From Thursday (October 1), it will be illegal to smoke with anyone under the age of 18 in a car.
The aim is to protect children and young people from the dangers of second-hand smoke.
Yet new RAC research reveals the vast majority (92%) of motorists do not have confidence that the ban will be effectively enforced.
A similar proportion (90%) are aware of it, but only 50% know it is coming into force this week.
"While the motoring public know this new law is coming, our data shows that a significant proportion are not aware just how soon it takes effect," commented RAC spokesman Simon Williams.
"It is worrying that nine in 10 motorists have concerns about the extent to which the new law is likely to be enforced. This is perhaps well-founded as traffic police officer numbers have fallen by nearly a quarter (23%) between 2010 and 2014 across forces in England and Wales, so it is hard to see how people flouting the law are going to be caught."
He added: "The new ban joins a raft of other laws that have been introduced in recent years such as making it illegal to undertake or hog the middle lane of a motorway. But without sufficient enforcement there is a real danger that these laws will quickly be forgotten by a large proportion of the motoring population."
Anyone caught flouting the new ban, which applies in England and Wales, will be handed a £50 on-the-spot fine.
Copyright Press Association 2015