New university students will be freed from paying £9,000 in tuition fees as early as this autumn if Labour wins the election, Jeremy Corbyn will say on Monday.

The Labour leader and Angela Rayner, his shadow education secretary, will say tuition fees will be completely abolished through legislation from 2018 onwards.

But students starting courses in September will have fees for their first year written off retrospectively so as not to encourage them to defer their studies for a year.

Labour said it would seek to provide free tuition for EU students and push for reciprocal arrangements at EU universities as part of the Brexit negotiations.

Students who are partway through their courses would no longer have to pay tuition fees from 2018, meaning those starting their final year of study in September would be the last cohort liable for the £27,000 of debts to be paid back when graduates pass an earnings threshold.

Labour said those students would be protected from above-inflation interest rate rises on their debts and the party would look for ways to reduce the burden for them in future.

“The Conservatives have held students back for too long, saddling them with debt that blights the start of their working lives. Labour will lift this cloud of debt and make education free for all as part of our plan for a richer Britain for the many not the few,” Corbyn will say.

“We will scrap tuition fees and ensure universities have the resources they need to continue to provide a world-class education. Students will benefit from having more money in their pockets, and we will all benefit from the engineers, doctors, teachers and scientists that our universities produce.”

Labour has said it will pay for the £9.5bn policy by raising tax on higher earners, making those with an income of more than £80,000 pay the 45p rate of tax and assigning a 50p rate to those bringing in more than £110,000 a year.

The party said its policy should give 18-year-olds another reason to register to vote before the deadline of midnight on Monday.

As well as abolishing university tuition fees, Labour will restore the maintenance grants the Conservatives abolished in 2016 and fund a free national education service.

Labour will give more details of its policies as Corbyn prepares to join Tom Watson, the deputy leader, for the launch of the party’s arts and culture policy in the north of England on Monday.

How do you register to vote? You must be registered to have a vote in the election.

You can register at gov.uk/register-to-vote, which requires you to answer 11 questions including name, address, national insurance number and whether you want a postal vote. The deadline is midnight on 22 May. To ​qualify ​register you must be a British, Irish or ​ citizen, a ​qualifying Commonwealth citizen resident in the UK, ​or a n EU UK citizen resident in the UK EU . ​or a UK citizen living abroad who has been registered to vote in the UK in the last 15 years. If you are a student you may be able to register to vote at both your home and term-time addresses, but remember that it is illegal to vote more than once.

The party has been boosted in the polls in recent days, with the Conservative lead falling back to nine percentage points in one survey by YouGov for the Sunday Times, after an apparent backlash against Theresa May’s social care proposals.

The Conservatives are trying to turn the agenda back on to the issue of leadership, with Ben Wallace, a security minister, accusing Corbyn on Sunday of “siding with Britain’s enemies”. Wallace made the remarks after the Labour leader faced repeated questioning in a Sky News interview about whether he would condemn the IRA, following newspaper stories about his links to figures in the militant group in the 1980s.

Corbyn said: “Bombing is wrong, of course all bombing is wrong and of course I condemn it … I think what you have to say is all bombing has to be condemned and you have to bring about a peace process. In the 1980s, Britain was looking for a military solution in Ireland. It clearly was never going to work. Ask anyone in the British army at that time.

“Therefore you have to seek a peace process. You condemn the violence of those that laid bombs that killed large of numbers of innocent people and I do.”

Asked to condemn the IRA without equating it to the deaths caused by British security services, Corbyn said: “And there were loyalist bombs as well, which you haven’t mentioned. I condemn all the bombing by both the loyalists and the IRA.”

If the Conservatives win the election, sources suggest Corbyn would want to stay on as leader if he matches Ed Miliband’s vote share from 2015.

Frank Field, who is seeking re-election as Labour MP for Birkenhead, called for any new leader to be chosen by the parliamentary party, not members, but with Corbyn’s manifesto as a starting point.

“In the event of a defeat on 8 June, Jeremy’s manifesto must be the point from which a new parliamentary Labour party alone chooses a parliamentary leader who is able to build trust and legitimacy with the electorate,” he said in a letter to the Guardian. “For the new parliamentary leader not to start from here, and to revert to Blairism, would miss the point of just how much Jeremy has changed centre-left politics. The test which must be passed in the new parliament is to combine a popular programme with a leader who possesses prime ministerial qualities.”