The Government’s Transport White Paper wants to cut cars from the “school run”. But the benefits of encouraging more walking or cycling to school could go well beyond the easing of road congestion. There could also be a big reduction in the stress levels and bad behaviour of many parents. That in turn could mean improvements in children’s behaviour.

Just the other day, while walking my daughter into school, I had to step between two parents who were coming to blows in a row over parking at the school gate.

They seemed oblivious to the wide-mouthed fascination of the children who were absorbing this “adult” behaviour.

Please do not get the wrong idea. The parents at my daughter’s school are pleasant and law-abiding. Usually the only assault you suffer is another request to buy tickets for the PTA raffle or quiz night.

The problem, as elsewhere, is those parents who not only drop their children off by car but insist on stopping or parking within feet of the gate. On this particular occasion, a mother stopped her car in the narrowest part of the road, blocking the way for allothers.

She was then berated by a cyclist. To his astonishment, the mother then began swearing at him and chasing him inside the school. She then physically attacked him; not a good example for the children. The next day, I noticed she was stopping in the same place again.

This was only the most extreme example of the problem the school has with those selfish parents who insist on parking as close as possible to the school. If they could, I am sure they would drive right up to the classroom door.

They park on the zigzag lines outside the school, apparently oblivious of the risk to all other children. They double-park, preventing others from passing. They park across the driveways of neighbouring houses, creating bad feeling between the local community and the school.

The school has tried many ways of stopping this. The car registration numbers of regular offenders have been published in the newsletters. But the offenders seem to know no shame and have not been discouraged.

Maybe it is time home-school contracts were extended to require considerate, polite and legal parking outside the school. But what sanctions could be used against miscreants?

Could it ever be fair to exclude a pupil whose parent parks badly? Maybe not. But put it a different way and it would not sound so unreasonable to exclude a child whose parent’s actions are endangering other pupils.

Ideally, the police would take tougher action and the courts would set appropriate community orders. I would love to see these parents (who oddly enough never help at PTA functions) having to paint the school toilets.

Building cycle sheds, creating cycle lanes and safer walking routes will probably not make any difference to these parents. Laziness is their problem, not excessive concern for the safety of their children.

So I think it is time for the Government to match their “failing schools” initiative with a clamp-down on “failing parents”. They should send teams of parking inspectors to schools with known problems. Bad drivers would be required to submit action plans for better parking and more considerate road use.

If they fail to improve they should be forced to undergo counselling or forfeit their driving licence. I am sure the Government could find the time to rush through a short Parliamentary Bill to take the appropriate powers. We could even have an OFSTEP (Office for Standards in Educational Parking) with a high-profile chief inspector such as Damon Hill or Michael Schumacher.

The benefits would be huge - not only in safety and health, but also in parenting. Instead of cursing motorists or fuming behind the wheel, parents could walk happily and peacefully to school, free to concentrate on conversation with their child.

They might even have time to do some mental arithmetic or spellings with them. Maybe the Transport White Paper will do more for pupil behaviour and standards than any of its education equivalents.

Mike Baker is the BBC’s education correspondent