The National Crime Agency said it was "asking for information we don't get".
It says it has also significantly stepped up efforts to seize dirty Russian money coming into the UK.
It has also launched investigations into British-based lawyers and accountants suspected of facilitating money laundering.
The NCA leads the UK fight against money laundering and criminal money, which it estimates could be worth up to £1bn a day.
A number of its investigations have led it to offshore firms registered in the Cayman Islands, which is a British Overseas Territory in the Caribbean and one of the world's largest financial centres.
Donald Toon, director of the NCA, revealed the Cayman Islands authorities had not co-operated when he had asked for information on who owned these firms.
He said that usually when his officers asked British Overseas Territories for help "we can generally get from them clear, unambiguous beneficial ownership information but we are having a difficulty with Cayman".
"The Cayman government is entirely aware of the UK concerns," he said.
In recent years the spotlight has been on tax havens linked to the UK following a series of global investigations involving nearly 100 media organisations, including the BBC.
The Paradise Papers exposed how wealthy and corrupt individuals used complex offshore structures to cover their tracks.
The NCA said there were now signs that criminals were finding new tax havens where they could exploit lax regulation and hide their links to corrupt assets.
These were jurisdictions "well beyond the British Overseas Territories". Mr Toon called them "small island nations" where "people are able to register companies but are much more difficult to penetrate in terms of getting access to the information" on beneficial owners.
He did not say where.
Mr Toon also said the NCA had significantly stepped up its work to identify and seize corrupt Russian assets in the UK - but it was yet to use new powers, known as Unexplained Wealth Orders, against them.
Unexplained Wealth Orders, which came into force on 31 January, force wealthy people to explain the source of their assets if there is reason to suspect corruption.
"This is not quick work," Mr Toon explained, because rich criminals are experts at hiding their ownership of corrupt assets.
He revealed there were "a couple of dozen" active investigations into lawyers and accountants suspected of facilitating the flow of dirty money into the UK which he described as the "lifeblood of nearly all organised crime".
Asked if he was concerned that dirty money was being used to fund the private education of the children of corrupt oligarchs, Mr Toon said those private schools with charitable status have to carry out due diligence.
However, he said they rarely issue alerts to law enforcement.
Source: bbc.com
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