Ms Gina Miller alongside the Independent Workers Union of Great Britain (IWGB) had issued a legal letter questioning Ms May's "confidence and supply" agreement with the Democratic Unionist Party (DUP) after her Conservative party lost its majority in the June general election.
Ms Miller believes the agreement, which included sending one billion pounds to Northern Ireland as part of the deal with the party, can be approved only through a vote in Parliament.
"It beggars belief that, neither at the time the government sealed its dubious deal with the DUP in exchange for their votes in the Commons, nor at any point since, has the government made it clear that the one billion pounds of taxpayers' money for Northern Ireland could only be handed over following Parliamentary approval," she said.
Ms Miller, born Gina Nadira Singh in British Guiana (now Guyana) to Guyana's former Attorney General Doodnauth Singh, has been a vocal campaigner against the government as part of a "Best for Britain" drive.
In response to her latest challenge, the UK government has conceded that it does indeed need the approval of Parliament before handing over the money to Northern Ireland, often described in the media as "cash for votes" as the Theresa May led government is dependent on the backing of the DUP's 10 MPs to win key votes in the House of Commons.
The UK's Treasury Solicitor, Jonathan Jones, said in his response that the government intends to use "long-established procedures, under which central government requests the grant of money by the House of Commons" and that there will be "appropriate parliamentary authorisation".
"No timetable has been set for the making of such payments," he noted.
Dr Jason Moyer-Lee, general secretary of the IWGB, said: "Many IWGB members' jobs depend on public money, like foster care workers and low-paid outsourced university staff.
"Yet, when it comes to keeping themselves in power, this government's fiscal discipline quickly dissipates. There's undoubtedly a need for increased social spending throughout the UK but this should be on a basis of fairness; not self- serving party politics."
While no Tory MPs are expected to rebel in such a parliamentary vote as the release of the one billion pounds is essential for the survival of the Tory government, any debate on the issue in the Commons is likely to be seen as another embarrassment for the Theresa May led regime.
The government is already faced with the prospect of a tough vote on legislation aimed at ending EU law's supremacy in the UK.
The EU (Withdrawal) Bill, which the government previously referred to as the Great Repeal Bill, overturns the 1972 European Communities Act which took the UK into the then European Economic Community.
It will also convert all existing EU laws into domestic ones, to ensure there are no gaps in legislation on Brexit day.
Opposition Labour says it will oppose the bill, claiming it represents a "power grab" as it will give the government powers similar to those used by medieval monarchs and has tabled a series of amendments.
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