Shadow chancellor John McDonnell says strong growth will pay for plan and reiterated that 95% of people would face no income tax rises after a Labour victory

Labour will aim to help tens of millions of people who are struggling on lower incomes by cutting the rate of VAT if it wins the general election, the shadow chancellor John McDonnell has told the Observer.

The new pledge to use the proceeds of future growth to reduce VAT from its current 20% level came as Theresa May and her senior ministers appeared to be at loggerheads over the Conservatives’ own tax policies, adding to an impression that the Tories are suffering a bout of late campaign jitters before polling day on Thursday.

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As the parties prepared their final pitches amid signs that the polls continue to narrow, a confident McDonnell reiterated his message that 95% of people would face no rises in their income tax bills under a Labour government.

But in a high-stakes move, he went further, saying his priority would be to deliver a “fair tax system” under which income tax rises for the highest earners would be followed by VAT reductions for all, when economic growth allows. Such a reduction, he said, would deliver the greatest proportionate benefits to those on low and middle incomes.

“The concept of fairness is at the heart of everything we do,” the shadow chancellor said. “When it comes to tax it will always be a fair tax policy. And if I can reduce the burden of taxation on middle and low earners I will do it as we grow the economy. I will do it.”

Asked what he had in mind, he added: “I think VAT is a real problem for many people. When we come out of Europe there is more flexibility on VAT, particularly in terms of the lower levels.”

The commitment is bound to be attacked by the Tories as further evidence that Labour lacks economic credibility and that Jeremy Corbyn and his team are making promises that the country cannot afford. McDonnell sought to address concerns over Labour’s economic competence by releasing a letter signed by 129 economists, backing its manifesto plans, which is published in the Observer.

On the timing of a VAT reduction, McDonnell said: “We will see how the economy grows. There are two ways we can share the benefits of prosperity. One is by making sure people get decent wages and the other is making sure the most regressive elements of the tax burden are reduced.”

He also revealed that a Labour government would hold a special “summer budget” before the parliamentary recess in July to implement key planks of its ambitious economic manifesto, including big rises in spending on the NHS and schools, and the abolition of student tuition fees.

He said he had recently held meetings with senior Treasury officials, including the permanent secretary, Tom Scholar, to discuss Labour’s plans and practical preparations, which would be implemented if Corbyn were to confound his critics and win on 8 June.

“We had a serious discussion about the policies we want to prioritise, the budget, the timing of it. It is all doable. That [having such meetings] is the norm ahead of an election. There is nothing exceptional about that. The objective is the preparations for government. We hit the deck running. You never take anything for granted, you don’t take votes for granted but you have to make the preparations.”

The last Opinium/Observer poll before election day suggests Labour is continuing to close the gap on the Tories. It puts the Conservatives on 43% (down two points) with Labour up two points on 37%. That lead would still deliver an increased Tory majority.

Other polls show widely differing results. One taken by Survation for the Mail on Sunday gave a Tory lead of one point and ComRes for the Independent and Sunday Mirror gave the party a lead of 12 points.

In mid-April, Opinium put the Tory lead at 19 points. While May is still well ahead in the personal ratings, with 42% of voters saying she would make the best prime minister, against 26% for Corbyn, the Labour leader’s public standing has improved during the campaign, while May’s popularity has declined. Some 40% of voters say they now have a more positive view of Corbyn, against 16% who say it is more negative, while 38% say their view of May is more negative, compared with 21% who say it is more positive.

On Saturday the prime minister appeared to slap down her defence secretary, Sir Michael Fallon, who had used the Daily Telegraph to say high earners would not face any income tax rises under the Tories. Fallon’s messages went further than the Tory manifesto which made no such commitment, and left the way open for possible rises. Campaigning in Yorkshire the prime minister insisted her party’s position was unaltered. “Our position on tax hasn’t changed. We have set it out in the manifesto.”

The Liberal Democrat leader Tim Farron will on Sunday urge Labour supporters to lend his party their support in seats where only it can realistically defeat the Conservatives. “There are dozens of seats across the country where the only candidate that can beat the Conservative is a Lib Dem. If you live in one of those places, I need you to lend me your vote,” he will say.