The Financial Times says investigators employed by Nigeria's civilian president have named 15 London banks.
They are cited as possible depositories of hundreds of millions of dollars from more than $4bn (£2.76bn) allegedly looted by General Abacha during his four-and-a-half year rule.
The paper says the UK Government was asked four months ago to help track any money deposited in London but did not respond.
It quotes British officials as saying they lack the power to freeze accounts and seize documents until charges have been brought in Nigeria.
Prime Minister Tony Blair is understood to have promised Nigerian president Olusegun Obasanjo full co-operation.
Frozen out
Mr Obasanjo's administration has been going to great lengths to try to recover the money looted by Abacha and his associates.
Switzerland and Liechtenstein have, at Nigeria's request, frozen hundreds of millions of dollars in bank accounts traced to Abacha's family.
The Swiss Federal Banking Commission says almost a third of the money deposited with Swiss banks had first been banked in the UK, US and Austria.
General Abacha ruled Nigeria from 1993 until his death in 1998.
According to the current Nigerian government, he used a circle of family members, close aides and business associates to disperse the stolen cash.
'Bribery and corruption'
It was allegedly amassed by awarding contracts to bogus companies, accepting bribes and siphoning money direct from the Nigerian treasury.
In September, several leading banks in Switzerland were criticised by the country's regulators for accepting money from Abacha's family.
In a report, the Swiss banking commission said 19 institutions had had dealings with the Abacha regime.
The commission acknowledged that the banks had reported their suspicions of money-laundering to the authorities, but said they should not have accepted the money in the first place.