Jersey, Guernsey and the Isle of Man have announced they will voluntarily adopt public registers of the true owners of offshore companies incorporated in their jurisdictions.

In a joint statement, the three islands said they would introduce fully public registers by 2023. Campaigners welcomed the announcement as a victory for transparency and an “important first step” in the fight against tax evasion and money laundering, though they said key details needed clarifying.

The announcement follows years of scandals about the use of offshore companies. Public registers identifying the owners of anonymous shell companies are widely regarded by anti-corruption campaigners as essential to tackling economic crime.

The UK’s network of crown dependencies and overseas territories have been exposed as havens for dark money in recent years through the release of the Panama Papers and subsequent offshore scandals. Britain has come under pressure to impose reforms on its territories and former colonies.

Until now the crown dependencies had resisted public registers, saying they would introduce them only once such measures were considered a global norm.

This year the leaders of the three islands travelled to London to head off an attempt by the Labour MP Margaret Hodge and the Conservative MP Andrew Mitchell to amend Brexit legislation to force the dependencies to introduce registers. At the time they said the proposed amendment was inoperable and would compromise the islands’ relationships with the British crown.

Hodge and Mitchell said the new announcement was a first step towards ensuring greater transparency, but they threatened to continue their campaign for legislation unless aspects of the proposal were clarified.

In particular, they said the timetable for implementing the new registers by 2023 was “unacceptably long”, the proposals would grant banks and accountants access to the information before the public and the media, and it was unclear whether the data would be available free of charge.

“Until we receive the assurances we need and that we have set out, we will pursue our plans to introduce legislation enforcing open registers of beneficial ownership in these jurisdictions,” they said.

Naomi Hirst, a senior anti-corruption campaigner at Global Witness, said: “This positive move shows that we are finally seeing years of campaigning by civil society and parliamentarians take effect. Transparency is the new norm.

“The era of secrecy is a thing of the past and other tax havens must now make their own moves to bring the real people behind anonymously owned companies out of the shadows. Any state failing to do so will be left behind.”

Hirst echoed the MPs’ concerns about the delay in implementing the registers. “The proof will, of course, be in the pudding. We have some concerns over the timeframe and that the details could leave plenty of room to manoeuvre,” she said.

Last year Hodge and Mitchell ran a successful backbench campaign to force the UK’s overseas territories, including the Cayman Islands and the British Virgin Islands, to introduce public registers by 2020.

However, this year it emerged that the British government planned to interpret the amendment to require the introduction of the registers by 2023 if the territories failed to do so themselves by 2020.