The government could be heading for a defeat in the Commons thanks to the efforts of Barking MP Margaret Hodge.
A crunch vote on money laundering is set to take place on Tuesday, May 1.
Dame Margaret is heading up a cross-party group which has tabled an amendment that would mean a companies based in British Overseas Territories would be listed on a public register.
It is hoped this would make it easier to trace the assets of criminals profiting from illegal practices such as people and drugs trafficking.
She has warned of “ever increasing” levels of money laundering happening in British Overseas Territories which include the Cayman Islands, British Virgin Islands and Bermuda.
In total 39 backbench MPs have signed the draft, which Dame Margaret has tabled alongside Conservative MP and former chief whip Andrew Mitchell.
The draft has the support of other senior Conservatives including former chancellor Kenneth Clark and Nicky Morgan.
Liberal Democrat leader Sir Vince Cable, former Labour leader Ed Milliband, the SNP’s Westminster leader Ian Blackford and Green Party co-leader Caroline Lucas have all pledged their support.
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