A group of Tory and Labour backbenchers are increasingly confident they can force Theresa May to introduce public ownership registers in Britain’s overseas territories in an attempt to prevent them from being used to hide “dirty money”.

Nineteen Conservative MPs have signed an amendment scheduled for debate in the Commons on Tuesday – theoretically a sufficient number to defeat the government, which has halted plans to implement a transparency measure originally proposed by David Cameron and George Osborne in 2013.

The Labour MP Margaret Hodge, who is one of the two principal backers of the amendment, said: “There is a spectrum of activity that starts with tax avoidance and then quickly goes on to money laundering and organised crime. Britain and its overseas territories have become the jurisdiction of choice for dirty money because of the secrecy of our offshore ownership laws.”

More than half of the offshore companies referred to in the Panama Papers were set up in the British Virgin Islands (BVI), according to Transparency International. The jurisdiction allows people to register companies in secret, prompting accusations that it is easy to hide cash and assets without external scrutiny.

Conservative supporters of the amendment to the sanctions and anti-money laundering bill are led by Andrew Mitchell and include the former cabinet ministers Nicky Morgan, Dominic Grieve, Stephen Crabb and Ken Clarke. The SNP’s Westminster leader, Ian Blackford, and the Liberal Democrat leader, Vince Cable, are also backers.

Mitchell said he was hopeful the government would recognise the strength of parliamentary opinion on the subject and find a way of “elegantly getting off the hook”.

He said: “The argument that the registers are available in private to UK authorities is insufficient. Public registers allow reporting and discussion of these matters by the media and civil society, as was demonstrated by debate that followed the leak of the Panama Papers.”

No 10 said on Friday it was studying the amendment carefully, prompting speculation that ministers may attempt to broker a compromise. “We want to analyse its effectiveness. This is an important issue and one we want to get right,” the prime minister’s spokesman said.

There are 14 British overseas territories, with a combined population of 350,000. Several have become major offshore financial centres, including Bermuda, Cayman Islands, Gibraltar and the BVI.

The overseas territories have introduced private central registers of ownership, which are accessible to UK law enforcement and tax authorities. The amendment calls on them to make those publicly available by December 2020, or have UK ministers impose that requirement upon them via orders in council.

Some of the territories have expressed opposition to the imposition of public registers, with one leading offshore centre saying it would cost its public purse $100m (£72m) a year.

In March, in a previously unreported submission, the BVI government told British MPs debating the bill that such a move “without consultation or consensus effectively disenfranchises the BVI legislature and its electorate creating resentment and damaging the historically strong relationship between the BVI and the UK”.

It said the territory was still recovering from the impact of Hurricane Irma and could not afford to deal with the effects from lost revenue. The BVI called on the UK government “to foot the bill or see a crisis in the BVI’s public services. Over the next 10 years this could result in an additional funding gap of $1bn.”

Proponents of the amendment have lobbied government ministers. In an attempt to allay Foreign Office concerns about introducing the disclosure measure so soon after the hurricane, the backbenchers agreed to leave the timing for implementation until 2020.

The sanctions and anti-money laundering bill is nearing the end of the parliamentary approval process, with its report and third reading in the Commons scheduled for Tuesday, having passed through the Lords.