Now Opposition parties plan to join forces to derail the attempted fix, in what threatens to be the first autumn Parliamentary clash over leaving the EU.
At stake is the extent of the Prime Minister’s power, through the Repeal Bill, to force through up to 1,000 “corrections” to EU law without MPs necessarily voting on them.
The vast number of statutory instruments (SIs) to be passed – some under “Henry VIII” powers – has already provoked accusations of a Government power grab.
The alarm has been raised over the protection of rights for British workers and consumers, lower environmental standards and curbs on the devolution of powers across the UK.
For example, Ms May has vowed workers’ rights will be protected, but has declined to say whether that will be enshrined in law – and has made no promise at all about food standards.
One source involved in the battle over the make-up of the committee said: “If the Tories go ahead with this, there will be a dust-up in September, because we will bring it to a vote in the Commons.”
The controversy comes as the Prime Minister returns from her summer holiday attempting to stamp her authority on a Cabinet “on manoeuvres” over Brexit policy in her absence.
Chancellor Philip Hammond and Liam Fox, the International Trade Secretary, wrote a joint article, insisting Britain would not seek to remain in the EU “by the back door”, in an attempted show of unity.
However, the pair remain split over the extent of a transitional deal which much of the Cabinet is seeking, for up to three years from withdrawal day in 2019.
Meanwhile, Anna Soubry became the first Conservative MP to threaten to quit the party if Ms May fails to “confront the ideologues” and continues to push for a hard Brexit.
The Commons row centres on the obscure Committee of Selection, which has the crucial task of arranging which SIs will be pushed through Parliament and when.
In the last Parliament, the Conservatives claimed five of the nine MPs on the committee, but officials have advised they are entitled to four only, after their Commons majority was destroyed.
Nevertheless, when talks broke up in acrimony as the summer recess began, the Tories were still insisting on five MPs – and the power to defeat the other parties.
The source added: “The Tories are trying to pretend the election didn’t happen and that they still have a majority – and, therefore, should have the majority on this committee.
“That would be obnoxious in the normal course of things but, in the context of a Parliament likely to be passing massive amounts of legislation through statutory instruments, it becomes an outrage.”
A second source agreed a September showdown was looming over the committee, saying: “The Government has to accept it does not have a majority.
“This is one of the biggest problems the Government faces and the reason why it hasn’t been able to get any business through since the election.”
The Government has insisted SIs will only be used – sometimes without a vote by MPs – to “correct” EU law where it is necessary to incorporate it successfully onto the UK statute book.
However, they have admitted there are no specific restrictions in the EU Withdrawal Bill, or Repeal Bill, to prevent ministers also changing aspects of law they “do not like”.
Some could be changed using Henry VIII powers, so-called because they date back to a 1539 law allowing the Tudor monarch to govern by proclamation, without consulting MPs.
Moreover, the full extent of the power grab is unknown, because the Bill will deliver the power to act over aspects of Brexit where policy will hinge on the outcome of Brussels negotiations.
Most of the SIs, or delegated legislation, will fall under the “affirmative procedure” – giving MPs a vote – but some will not, the notorious Henry VIII powers.
The battle over the Committee of Selection sets the scene for an autumn of trench warfare when the EU Withdrawal Bill arrives in the Commons on 7 September.
Pro-EU Labour MPs will attempt to amend it to keep Britain in the EU single market for a transitional period and are wooing Conservative rebels to try to defeat the Government at the outset.
The Conservatives and Labour have failed to agree the usual “pairing” system that allows MPs to miss less important votes while they are travelling, or visiting their constituencies.
It means the Government may have to force every MP to attend every vote to avoid unexpected parliamentary defeats, taking Parliament back to the wars of attrition of the late 1970s.
The Bill will convert EU law into UK law before Brexit is complete in 2019, before the Government proposes which bits should be retained or junked.
A Conservative party spokesman declined to comment on the negotiations to decide its representation on the Committee of Selection.
The body decides whether the Government has an all-important majority on committees for both SIs and legislation – without which, ministers are unlikely to press ahead.