With the school holidays over and children ready to be ferried to and from school by family car and the much vilified 4x4 “Chelsea tractor”, it’s back to hell this week for the school-run mum — and millions of ordinary motorists. Despite efforts to persuade parents to car share, use public transport and cycle or walk children to school, one in five cars on the road in urban areas at 8.50am will be on the school run.

Greta Wynn Davies, 34, a music video artist and mother of Maya, 5, and Sienna, 3, will be part of the daily scrum, driving her girls in her Jaguar XJR two miles from their home in Islington, London, to Dallington, an independent primary school. “I walked my oldest child to and from nursery,” says Wynn Davies. “I did try to get the girls into school locally. But the school you choose for your children is important and Dallington turned out to be the best one for them.”

Parents put concerns for their children’s safety (36%) top of the list of reasons for sticking with the school run with quickness of journey (32%), lack of public transport (18%) and too far to walk (16%) also cited. Wynn Davies could tick all those boxes.

Dallington is too far for the girls to walk and three buses would be required if they went by public transport. “Buses would also add an hour to the journey each way,” she says. “That’s time when I could be earning.”

So she braves the congestion every day. Though she walked to primary school as a child with her older brother, she feels — pointing to the recent murder of little Rory Blackhall on his way to primary school — that children face greater dangers these days. The girls will be 14 before she allows them to use public transport by themselves.

There is no gridlock in the street outside Dallington when parents drop off their kids. Wynn Davies is thankful for that having witnessed the bumper-to-bumper chaos on the now notorious Fitzjohn’s Avenue in Hampstead, north London, when thousands of parents descend on its numerous independent nurseries and schools.

In one of the most affluent areas of the capital parking attendants, responding to complaints from residents about illegal parking, do daily battle with school-run mums. Attendants recently rated Fitzjohn’s Avenue among London’s top 10 abuse and assault hotspots.

In May, Karen Webb, 42, whose son Tom, 6, attended Devonshire House, one of the Fitzjohn’s Avenue’s independent schools, organised a “walk and cycle” protest against parents driving their children to school. “There are 28 schools within a mile’s radius of Fitzjohn’s Avenue,” says Webb, who takes Tom to school by Tube. “The congestion is horrendous.”

Webb’s concerns are mainly environmental and her campaign infuriated some mums. However, she argues that she is not anti-car and accepts that school-run mums can be an easy target for local authorities who ought also to pursue other road users in campaigns to cut congestion and pollution.

John Thane, a Camden councillor, says schools are now having to come up with green travel plans (GTP) to reduce car traffic. In one case, having a GTP was a condition of planning permission to expand school premises.

Walking groups, cycling groups, public transport use, minibus use and car sharing are all part of Camden’s approach. Thane is uncompromising in his assault on the school run. Parents might argue that the standards in state schools make sending children to the neighbourhood school impossible but Thane insists “it does not make sense to send your child to a school to which they cannot walk”.

And what of fears about the safety of children walking or taking public transport? “That fear is unhealthy,” says Thane. “How do children learn to be independent? There is a limit to the levels at which children can be mollycoddled.”

Tackling the school run was one of the reasons given by Ken Livingstone, the London mayor, for his £70m scheme that will allow children under 16 to travel by bus for free in the city from this month. “This will continue London’s move away from car journeys,” he said. “It should also cut congestion, pollution and accidents by reducing the school run.”

Sir Peter Lampl, chairman of the Sutton Trust education charity, insists the push for more walking, cycling and public transport use is pointless. Parents, he argues, do not think they are safe alternatives.

Yellow American-style school buses are Sir Peter’s solution to school-run hell. Yellow bus schemes have already been piloted in various parts of the country and a large-scale pilot is currently underway in West Yorkshire. But Sir Peter says the school bus proposal is hampered by the fact that the issue falls between three government departments — education, transport and the environment. “It’s everyone’s problem and no-one’s problem,” he says. “What’s required is a bit more imagination.”

What’s also required is rather awesome initial investment. One report, produced by the Sutton Trust and the left-leaning Social Market Foundation and the right-leaning Policy Exchange, says a national bus scheme would cost £183m, a large sum for government to contemplate even with projected gains of £450m.

Fifty per cent of children in America go to school by bus compared to only 6% in Britain. Interestingly, Wynn Davies and Webb are both intrigued by the yellow bus proposal. However, Webb is sure that there is no single solution to the problem. Every school-run parent, she argues, has to look at the possible alternatives.