Just hours before it was due to take place, the UK Government postponed the division on a Bill designed to protect the financial services industry after Brexit.
The measure needs to be in place by Brexit day – scheduled for 29 March – in preparation for a possible no-deal departure from the European Union.
The delay creates another major headache for Mrs May, who faces a daunting task in driving through Brexit-related legislation regardless of whether or not she can win a Commons majority for her withdrawal agreement with Brussels.
More than 20 Tory MPs had been preparing to defy their whips to support a cross-party demand for financial transparency by crown dependencies and British overseas territories.
Ministers shelved the vote after Jersey, Guernsey and the Isle of Man warned the amendment to the Financial Services (Implementation of Legislation) Bill ran counter to their constitutional relationship with the UK.
In the face of certain defeat the Government pulled the business for yesterday.
The Bill now has to be rescheduled for debate with a view to getting it on to the statute book by 29 March.
Labour accused the government of being in chaos and providing laughable explanations for the delay.
John McDonnell, the shadow chancellor, said the move was further evidence of the government being “incapable of getting its business through Parliament”.
The anti-money laundering amendment requires overseas territories to compile a public register showing the true ownership of companies based there by the end of next year.
It has been championed by the Conservative former international development secretary Andrew Mitchell and senior Labour MP Dame Margaret Hodge.
Mr Mitchell said: “This amendment is an important continuation of the G8 agenda on transparency and openness to combat money laundering and tax evasion.
“In the face of certain defeat the Government have pulled the business for today, but the business will return and so will this important amendment.
“Parliament decided last year that the British Overseas Territories should adopt open registers of beneficial ownership and so now should all members of the British family.”
The Treasury said it wanted to give the amendment “proper and thorough consideration”.
A spokesman said: “The government will not move the Bill today but will reschedule it to ensure there is sufficient time for proper debate.”
The Bill is part of the Government’s no-deal Brexit planning, allowing the UK to adapt to changes in EU financial services legislation.
Downing Street insisted the Government would ensure it had the powers in place if needed in a no-deal scenario.