The Queen must open up her full financial records to the public in the wake of revelations about her investments in the Paradise Papers scandal, Labour has said.

In an exclusive interview with The Independent, Shadow Chancellor John McDonnell said information that showed the Queen had invested millions in an offshore tax haven proved “the culture of tax-avoidance” has “permeated everywhere”.

He said the monarch’s advisors had badly embarrassed her, and in particular demanded an apology of the Tory cabinet minister ultimately responsible for overseeing her finances, Sir Patrick McLoughlin.

As the Government closed another round of Brexit talks, Mr McDonnell also called on ministers to release legal papers that are expected to indicate that Brexit can be unilaterally reversed by the UK.

Mr McDonnell’s words came as he prepared to make a speech setting out how the Government may have lost out on £37bn from dividends in privatised companies – which he promised to nationalise in the first five years of a Labour government.

The Paradise Papers – a dossier of 13.4 million documents – sent a shockwave across the world when they revealed tax-avoidance of major global figures including members of the royal family. In the papers the Duchy of Lancaster, the private estate of the Queen, was found to have invested millions in offshore arrangements in the Cayman Islands and Bermuda between 2004 and 2005. There is no suggestion that those involved acted illegally.

The documents also traced a small portion of the Queen’s investments – £3,208 – to the rent-to-buy firm BrightHouse – a company that has previously been accused of exploiting poor customers with high interest rates.

At the time Buckingham Palace highlighted that the Queen’s investments are fully “audited and legitimate”, adding that she “voluntarily pays tax on any income she receives from the Duchy.”

But the Shadow Chancellor said: “It just demonstrates that there’s a culture that has been developed even amongst advisers to the Queen that this is acceptable.

“The whole culture needs to change and that’s what we’re challenging.”

Asked whether the Queen’s full financial records should be made public, Mr McDonnell told The Independent: “I publish my income tax returns, I think we should be open and transparent with everyone. Jeremy does the same. We expect Theresa May and Philip Hammond to do the same as well.”

Pressed again on the financial affairs of the Queen, whose officials do publish some tax data, he added: “I think we should have complete openness and transparency for everybody that level in society – yeah.

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“It’s not a matter of forcing it, I do it voluntarily. We’ve said everyone earning over a million should publish their income tax. Why not?”

On a wider scale, Mr McDonnell said the overall revelations were “shocking” and said individuals have “got to realise their moral responsibilities” to pay for essential public services. “I think more and more people are beginning to recognise that there’s a strata of society that actually don’t accept their moral responsibilities.

“There will come a time in this debate when we will force through proper reforms. The issue we’ve been campaigning on for the last two years is to ensure the transparency of trusts – publication of beneficiaries.”

Elsewhere in the interview, the Shadow Chancellor also said that on Saturday he would deliver a speech at an economic conference in Lincoln, claiming that private companies have paid out £37bn in dividends to shareholders since 2010. He will say that the money could have been invested in public services as he restates Labour’s plan to nationalise key British utilities and infrastructure.

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The Labour research – conducted in consultation with the independent House of Commons Library– shows that in 2017 privatised firms paid out a total of £4.8bn in dividends.

According to the analysis, since 2010 more than £10bn has been received by National Grid shareholders, £6.3bn by BT shareholders, and £5.2bn by investors in Centrica, which owns British Gas.

“These figures show what could have gone into investment in these public services in order to expand and improve them or keep their charges down,” he will say.

“The last seven years of austerity has seen working families suffer from stagnant wages not being able to keep up with prices of items like energy bills, and underfunded public services – yet billions has gone into the hands of shareholders.

“The next Labour government will call an end to the privatisation of our public sector, and we will look to bring back into public ownership many of the vital services sold off by the Tories, which are undermining the living standards of millions of working households.”

Mr McDonnell said the companies would come “back in” to public ownership over the life of a Parliament should the party win the next election.

On Brexit, the Shadow Chancellor said the Government should publish legal advice on the revocability of Article 50 – the legislation invoked in March that kicked-off the two-year countdown to Britain’s exit from the bloc.

His demand followed an intervention from the British legal expert who wrote Article 50 and accused the Prime Minister of “misleading” the public over whether Brexit can be reversed. Former diplomat Lord Kerr condemned Ms May for making a “political decision” to withhold the truth, that the Government can unilaterally stop Brexit any time it likes.

Asked about Lord Kerr’s comments, Mr McDonnell said: “The legal opinion should be published now.

“I know in some instances Government has argued that legal opinion are sacrosanct because they are advice to ministers. What we’re saying is be completely open and transparent now then let people judge themselves.”

The Shadow Chancellor also said that a general election “could come at any time” but said he did not underestimate the Tories’ ability to “cling on to office”.

“That’s my real worry,” he added. “They are rendering this country into a state that I think will be difficult for a Labour government to tackle, but we will. Everyday that they remain in office the country will suffer.

“We are in it for the long haul. If this Government goes, if this Government collapses we’re ready to take over tomorrow.