Parents in Bristol and Kingston upon Thames are the latest to demand new neighbourhood schools for their children, amid claims they are being forced to go private or travel long distances for a suitable education.

They want local authorities to support their call for additional state schools to be opened in their areas. In both cases, education chiefs believe they have a valid case.

The families join a growing number of campaigners around the country demanding top-quality, local schools. Parents in Dulwich, south London, are already liaising with Southwark council over the creation of a new secondary.

In Kingston, campaigners claim there will be too few secondary places for the growing population within 10 years, justifying the need for a new school. Parents say there is no local school serving the northern part of the London borough, forcing children over the border to Richmond, where schools are already over-subscribed.

Sue Bradbury, who is leading the campaign, said: “Councillors seem to believe that the fact that this is a fairly affluent area and parents can opt to go private absolves them of any responsibility to do anything.

“Kingston comes top of the league tables but if you took away the Tiffin grammars and the independent schools, we would be a long way down the list. There is no room for complacency, and even well-off parents do not necessarily believe in paying for education.”

In Bristol, families in the north-west of the city are complaining they have no local school which offers acceptable standards. The schools that are within travelling distance are already over-subscribed or fee-paying.

Jan Elliott, who was forced to send her daughter to a school in South Gloucestershire, said: “Outside of London, Bristol has the highest proportion of private schools, but that is not the answer.”

John Ashton, chairman of Bristol’s education committee, said the city council has approached the Department for Education and Employment for funding to carry out a feasibility study.

“We are still waiting to hear the outcome of that request. While there is a geographical need for a new school, we do have surplus places in the city,” he said.

John Heamon, education committee chairman at Kingston, said education chiefs sympathised with parents, but it was unlikely that the Government would allow the building of a new school. “It is possible we will have to expand existing schools,” he said.