A victory for Ken Livingstone in next month’s London mayoral elections will apparently mean better exam results, less educational inequality and greater security in the capital’s schools.

A fine set of aims, certainly. But perhaps a trifle ambitious considering his office has no formal responsibility for schools.

However, that detail has stopped neither him nor his main rivals from making schools a major issue in their mayoral campaigns.

In the Labour mayor’s young people’s manifesto, Mr Livingstone promises to work with the police and fire services to ensure that branches of their cadet schemes are set up in every London secondary. He also wants schools to work with police, local councils and community groups to reduce gang activity and violent youth crime.

The mayor says he will ensure schools suffering from these problems will have priority use of scanners to detect knives and guns. More police will be based in them.

Pupil safety is an equally big issue for Boris Johnson. The Conservative rival to Mr Livingstone also believes more youth clubs are the key to tackling London’s gang culture.

“My number one priority is to make this place as tranquil as it was when I was a kid,” he said.

Mr Johnson said clubs should offer young people academic support as well as sporting activitiies. He would like the Government to offer more support for literacy in schools, particularly those in which many pupils speak English as a second language.

Exactly how he expects to exert his mayoral influence over the Department for Children, Schools and Families (DCSF) has not been made clear.

But the sceptic might find it equally difficult to understand how Mr Livingstone can claim credit for GCSE results rising faster in London than elsewhere in England, or for new school buildings.

Brian Paddick, the Liberal Democrat candidate, was a little more straightforward. “As the Mayor of London, I shall not have direct powers over education and schools,” he told The TES.

“However, my style of government will very much involve working with the 32 boroughs responsible for children and young people’s services.”

Away from the intrigue of the mayoral election, contests are taking place on May 1 in another 55 local authorities that really do have power over schools. England’s 36 metropolitan districts are all up for election, as are one-third of the seats in 19 unitary authorities.

Power over schools has drained steadily from town halls to Whitehall over the last two decades.

Now, however, there are signs that the pendulum may have begun to swing in the other direction.

The DCSF is making a point of giving local councils more responsibility for education while both opposition parties talk of devolving more power.

If David Cameron wins the next general election, political control over a local council could have a direct impact on schools.

The Conservatives have said that the fate of secondaries with low GCSE results will rest partially on how long the relevant local authority has been under the control of a single political party.

Crucially, there is doorstep evidence that people still believe that for schools the buck stops locally. Asked whether local people blamed Westminster or their local council if their neighbourhood school was underperforming, Tim Pickstone, Association of Liberal Democrat Councillors chief executive, said: “I think they will blame the LEA.”

HOW THEY STAND ON SCHOOLS

Ken Livingstone (Labour)

- Police and fire cadet forces in every London secondary;

- More police, and gun and knife detectors based in schools;

- More youth clubs.

Boris Johnson (Conservative)

- More youth clubs;

- Pressure on Government to provide more funding for literacy in schools;

- Oppose the closure of playing fields.

Brian Paddick (Liberal Democrat)

- Intelligence-led policing to break knife and gun culture;

- Reinforcement of the anti-bullying work done by the Greater London Authority;

- Better sports and leisure facilities for young people.