Jeremy Corbyn has surprised almost everyone, possibly including himself, by moving from rank outsider to the bookies’ favourite in the Labour leadership race.

Headlines abound about his plans to end austerity, drive up public spending, embrace the trade unions and prosecute Tony Blair for war crimes.

But what of schools? What would a Corbyn-led Labour Party actually attempt to do in education? It’s not completely clear just yet, but here’s a rough guide:

1. A National Education Service

The Islington North MP wants to establish as National Education Service, modelled on what the NHS does for healthcare. It will ensure lifelong learning that will be “every bit as vital and free at the point of use as our NHS”.

2. Free schools and academies

Mr Corbyn wants to “rethink” the role of free schools and academies, which he says are locally unaccountable. They would almost certainly be moved back under local government control.

3. Apprentices

He has promised to pay the minimum wage to apprentices.

4. Lifelong learning

He has pledged to provide more money for adult learning, paid for by raising money by increasing the corporation tax by 2 per cent.

5. Tuition fees

He would scrap university tuition fees entirely in favour of a return to grants. This would be resisted heavily by universities, many of which are currently campaigning for these fees to increase. Some estimates have put the cost at more than £10 billion.

6. Private schools

Like many in the Labour party, Corbyn is keen abolish the charitable status enjoyed by private schools, although he has admitted it would be difficult to achieve.

7. Childcare

Sure to be a winner among parents, Mr Corbyn has called for universal free childcare in the early years.

8. Grammar schools

If rumours that he divorced his wife after he disagreed with her wishes to send their son to a grammar school are true, it doesn’t look good for the countries remaining selective state schools.