Banks have been given just days to say whether or not they did deals with the law firm at the centre of the Panama tax dodging allegations.
Regulators have given 20 UK banks and financial firms a week to probe their own affairs.
Earlier this week RBS effectively admitted that it did not know if it had ever had a relationship with Mossack Fonseca.
Sources at the bank said that it had launched a wide-scale review, going back decades, to discover if it had ever used the law firm.
An RBS-owned offshoot, Coutts, has already been named as having used Mossack Fonseca, following the largest data leak in history.
Meanwhile, David Cameron has defended his Government's record on tax as he faced increased scrutiny on his own family's affairs.
He also faced fresh criticism after it emerged that he successfully watered down the effect of EU transparency rules on trusts, despite warnings his actions could help would-be tax dodgers.
Mr Cameron told students during a visit to Exeter: "Britain has been an absolute leader on this and we will continue to do it."
But he faced criticism for not taking questions from journalists, amid accusations his ministers announced plans to spend £9m sending a pro-EU leaflet to every house in the UK to try to distract from the tax controversy.
Labour's deputy leader Tom Watson said that the Prime Minister "might have thought he could fudge his position" on his own tax affairs but predicted the issue would not go away.
The Financial Conduct Authority (FCA) has told banks and businesses that they have until April 15 to investigate ties to Mossack Fonseca.
The leak of more than 11 million documents from the Panamanian law firm has sparked allegations of money laundering and tax evasion across the globe.
HSBC, Credit Suisse and Coutts Trustees denied claims earlier this week that they were helping clients avoid tax by using complex offshore structures.
In a statement, the FCA said: "As part of our responsibility to ensure the integrity of the UK financial markets we require all authorised firms to have systems and controls in place to mitigate the risk that they might be used to commit financial crime."
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