Former prime minister Gordon Brown is urging David Cameron to join other EU states to impose sanctions against British overseas territories and crown dependencies that continue to act as tax havens for the wealthy.
The Prime Minister is coming under pressure from development charities to use this week's anti-corruption summit in London to get tough on territories that refuse to establish public registers of company ownership.
Mr Cameron's position as host of the two-day summit was made more awkward after he was caught on camera branding two participating states - Nigeria and Afghanistan - as "fantastically corrupt".
The PM's comments, made to the Queen during a Buckingham Palace reception, were described as "embarrassing" by a spokesman for Nigerian President Muhammadu Buhari and "unfair" by the Afghan embassy in London.
After revelations about offshore financial activities in the so-called Panama Papers, Mr Cameron last month announced that the overseas territories and crown dependencies - like the British Virgin Islands and Jersey - had agreed to provide UK tax and law enforcement agencies with full access to company ownership details.
But charities have insisted they must go further and allow public access to registers, so they can be examined by journalists and NGOs.
Writing in The Guardian, Mr Brown said: "If we are to ensure no hiding places for tax evaders, no safe haven for tax avoiders and no treasure islands for the money launderers who hide an estimated 7.5 trillion US dollars (£5.2 trillion) of global wealth, we need the automatic exchange of tax information worldwide.
"In addition to a comprehensive European blacklist of tax havens as the first step to a global blacklist, we should agree that British overseas territories and crown dependencies that fail to comply cannot be excluded from the blacklist; and the UK should now require them to have public registers of beneficial owners.
"Britain cannot achieve this on its own. And with America currently resisting reciprocal tax arrangements, collective action by all 28 countries of the European Union to blacklist avoiders, impose sanctions and even levy withholding taxes - on our own overseas territories, if necessary - is currently the one game in town."
Adrian Lovett, deputy chief executive of development charity One, said Mr Cameron needed to get "tough" on flaws in the global financial system - including in the overseas territories - which allow the corrupt to salt away money which could otherwise be used to improve living standards in poorer countries.
"This week's anti-corruption summit is a real opportunity to clean up corruption, but the litmus test of success is whether the delegates agree to public registers of company ownership," he said. "Without this, the Prime Minister will have missed a golden opportunity to raise standards of financial fair play."
Labour deputy leader Tom Watson called for a "strong lead" from the PM to secure agreement on urgent financial aid for under-funded tax regimes in developing countries as well as providing help for overseas territories to end their "dependency on the financial services industry".
"David Cameron has said he won't call on UK territories to publish a register of beneficial ownership despite earlier promises to do so," said Mr Watson. "He needs to change his mind and fulfil those promises because tax avoidance will continue to thrive until the mask of anonymity that allows the owners of assets to disguise their identities has been removed."
Mr Cameron was caught on a broadcast camera chatting with the Queen, Archbishop of Canterbury Justin Welby and Commons Speaker John Bercow at an event to mark the monarch's 90th birthday.
"We've got some leaders of some fantastically corrupt countries coming to Britain," Mr Cameron told the Queen. "Nigeria and Afghanistan - possibly the two most corrupt countries in the world."
Mr Buhari's spokesman Garba Shehu later released a statement on social media: "This is embarrassing to us, to us say the least, given the good work that the president is doing. The eyes of the world are on what is happening here. The Prime Minister must be looking at an old snapshot of Nigeria. Things are changing with corruption and everything else."
A spokesman for the Afghan embassy in London said: "President Ghani and his Government since in office have taken major steps to fight corruption. Countering corruption is a top priority along security issues for the National Unity Government.
"We have made important progresses in fighting systematic capture in major national procurement contracts and are making progress on addressing institutional issues as well as issues related to impunity. Therefore calling Afghanistan in that way and taking bold decisions by NUG is unfair."
Downing Street played down the significance of Mr Cameron's remarks - pointing out that Mr Buhari and Afghanistan's Ashraf Ghani have each written an essay for a book to accompany the summit, in which they acknowledge the scale of corruption in their countries and discuss their efforts to tackle it.