Labour has unveiled new details of its plans to create a National Education Service (NES) if it wins the next election.

Part of this would see the current academy system overhauled, and shadow education secretary Angela Rayner made this the centre-piece of her speech at the Labour conference in Liverpool.

The proposals would swing the pendulum away from academy trusts and towards local authorities, but they are more nuanced than some Labour activists may have hoped.

Here’s what you need to know:

So Labour will get rid of all academies?

No, not under the plans that Ms Rayner announced yesterday, although many in her party wish it would.

Instead, her proposals could see a more gradual decline in the number of academies, which currently stands at 7,475, educating about half of children and young people in state schools.

Labour pledged that there will be “no new academies under the next Labour government”, and that existing academies will be able to return to local authorities “assuming there is capacity and desire to do so in the relevant local authority”.

If academies won’t be abolished, will Labour put them back under local authorities?

No - and Ms Rayner’s speech was very carefully worded to avoid saying this.

She told delegates that “we will use our time in government to bring all publicly funded schools back into the mainstream public sector, with a common rulebook and under local democratic control”.

What exactly this “local democratic control” consists of is not explained.

However, a report from Labour’s Early Years, Education and Skills Policy Commission to conference was clear that Labour does not yet have the answer to this question, saying that while transparency and accountability are important, “there is more for the commission to do”.

What about free schools?

Ms Rayner said a Labour government would end Michael Gove’s flagship programme.

In saying this, she is re-stating existing Labour policy that there will be no new free schools, as set out in its general election manifesto in 2015 and again in 2017.

Labour did not spell out what its plans would mean for existing free schools that are already open.

So what changes would Labour make to academies and local councils?

Angela Rayner proposed some significant changes.

The most important proposal is that academies would no longer be their own admissions authorities, and local authorities would regain responsibility for all school admissions in their areas.

Councils would also be able to order existing academies to expand where there is demand for places.

And with no more free schools created, councils would be allowed to open and commission new schools.

This would address the anomaly Ms Rayner highlighted in her speech where currently “councillors are left responsible for school places but without the power to create them”.

What would Labour do about areas of high-profile controversy around academies?

The Rayner reforms would also tackle two areas that have done the most to tarnish the reputation of academies: chief executive pay and contracts that are handed to people with close connections to the academy or trust.

Both are areas where the DfE has recently been taking action, putting the highest salaries under scrutiny and requiring advance authorisation of related-party transactions above £20,000.

Labour would go further, bringing in national pay rules to stop MAT executives “paying themselves fat cat salaries”.

However, setting the limit at 20 times the salary of the lowest-paid member of staff - as Labour is reported to have briefed journalists - could still allow CEOs to earn more than £300,000, based on the salary of someone earning the national living wage.

And Labour says it would ban related-party transactions.

What about multi-academy trusts?

Labour wants to “rein in” MATs by forcing them to abide by nationwide rules, and taking powers away from the trust level and giving them to individual schools.

The changes to admissions, CEO pay and related party transactions would clearly put limits on what MATs can do.

Labour’s briefing added that the party would “transfer responsibility for decision making and budgets back to schools, requiring every school to have a governing body of democratically elected parents, teachers, other school staff, community representatives, and to consult on any major changes in school policy or governance before they are introduced”.

Under Angela Rayner’s plans, multi-academy trusts would still exist, if in a denuded form.

But minutes after she sat down, delegates overwhelmingly voted for a policy that goes further, calling for the urgent development of “proposals to wind up MATs and turn over control and management of schools to locally democratically controlled structures”.

So is it now official Labour Party policy to abolish MATs? The answer is not clear.

When Tes asked Labour this question, a spokesperson said: “Proposals for primary legislation that will allow statutory regulation to override MAT contracts is being developed, and we will set out our policy in this area in more details in due course.”

Such primary legislation would be needed to strip MATs of powers in areas such as admissions; whether the legislation Labour is working on would extend to winding up MATs is not clear.