The Labour party has said it would force big companies to publish full tax returns to expose any “sweetheart” deals that firms arrange with the taxman to potentially reduce their tax bills.

Shadow chancellor John McDonnell said if Labour wins the next general election it would “close the loopholes through which large corporations swindle the public”. He said the “tax gap” between what companies should be paying and what is actually received by the exchequer amounts to some £36bn.

Successive governments, including Theresa May’s administration, have pledged to crack down on multinational companies gaming the international tax system to pay less tax. But accusations persist that some multinationals have been allowed to arrange so-called “sweetheart” deals with firms, including Google, Vodafone and Starbucks, to pay nominal sums to settle investigations into allegations of years of tax avoidance.

“Tax avoidance is a scourge on society that company secrecy laws help facilitate, and the Tories have done nothing to tackle it,” McDonnell said. “Labour will pour the disinfectant of sunlight on large company accounts, helping close down the loopholes and the scams that the tax dodgers rely on.

“The Tories are running a rigged economy for the super-rich and giant corporate tax dodgers. Only Labour will stand up for workers and small businesses to make our tax system fair and our public services like education and the NHS protected.”

Under Labour’s plans all companies with more than £36m in turnover or more than 250 employees would be required to file a complete tax return at Companies House along with annual accounts.

Labour argued it was unfair that large companies are able to hire armies of accountants and lawyers and “wine-and-dine senior civil servants” in search of sweetheart deals, while smaller firms pay their taxes when they fall due.

The publication of large company tax returns and related correspondence would expose any such deals, the opposition said.

When parliament returns after the Easter recess on Tuesday, Labour will also push to strengthen measures to tackle tax avoidance in the finance bill.

Peter Dowd, Labour’s shadow chief secretary, said: “The measures in the finance bill claiming to close tax loopholes do not go far enough and have gaping omissions, another Tory conjuring trick to hide their inaction in making sure that everyone, including the rich, pays their fair share of society’s upkeep.

“There is nothing in the government’s proposals to address the chronic lack of enforcement in the context of the wider regulatory problems. As usual, the Tories are playing rhetorically to the gallery.”

Responding to Labour’s announcement, Conservative party vice-chairman, Stuart Andrew MP, said:

“This government has a simple message for those who avoid tax: you must pay what you owe and we will make sure you do.

“After thirteen years of Labour doing nothing we have led the way on tackling tax evasion, avoidance and non-compliance, securing an additional £140bn in additional tax revenues since 2010.

“All Labour would do now is wreck the economy with higher taxes, half a trillion in additional borrowing and a leader who says we should not be afraid of debt.”