Mr Madoff told senior employees of his firm on Wednesday that “it’s all just one big lie” and that he was “finished”, according to a criminal complaint filed on Thursday night by the US Attorney’s office and the Federal Bureau of Investigations (FBI).

He allegedly went on to say that the business was “a giant Ponzi scheme” – a reference to Charles Ponzi, one of the greatest swindlers in US history – and estimated that the scheme had lost investors $50bn over many years – which would make the hedge fund one of the biggest frauds in history.

“There is no innocent explanation,” Mr Madoff said, according to the criminal complaint. He told the agents that it was all his fault, and that he “paid investors with money that wasn’t there”, according to the complaint.

He allegedly told his employees that he had, for years, been paying returns to certain investors out of the cash received from other investors.

Mr Madoff, 70, was charged with a single count of securities fraud and faces up to 20 years in prison and a fine of up to $5m if found guilty.

The criminal complaint was accompanied by a separate civil lawsuit filed by the US Securities and Exchange Commission (SEC), which accuses Mr Madoff of defrauding clients of his firm and seeks emergency relief for the victims.

“Our complaint alleges a stunning fraud – both in terms of scope and duration. We are moving quickly and decisively to stop the scheme and protect the remaining assets for investors,” said Scott Friestad, the SEC’s deputy enforcer.

The complaint details that as of Jan 7, 2008, Madoff’s investment advisory business had assets of $17.1bn, serving up to 25 clients.

Although Mr Madoff is thought to have few direct British links, he did open a London office in 1983, with Madoff Securities International becoming one of the first American members of the London Stock Exchange.

Stephen Raven, chief executive of Madoff Securities International said: “We only became aware overnight of the news relating to our Chairman, Bernard Madoff. Our business in London is not in any way part of Bernard L Madoff Investment Securities LLC. His major shareholding in our firm is a personal investment. Our business activities are not involved in any way with the US asset management company with which the reported allegations appear to be concerned. We do not have any further information beyond what is already in the public domain.”

In 2000, his market-making business BMIS partnered with Goldman Sachs and Merrill Lynch to the form the new Primex Trading platform, one of the early rival electronic exchanges to the main bourses which eventually fell by the wayside following a partnership with NASDAQ.

BMIS is also credited with ending the old practice of quoting New York Stock Exchange-listed securities in eighths of a dollar in 1997, instead listing them in sixteenths.

Mr Madoff began BMIS with just $5,000 of savings from jobs lifeguarding at Rockaway Beach and installing sprinkler systems.

The firm grew to become a leading market maker, with brother Peter, nephew Charles, niece Shana, and sons Mark and Andrew all involved in the business at some stage in recent years.

His firm’s website claims that BMIS ranks among the top one per cent of US securities firms, and states that “clients know Bernard Madoff has a personal interest in maintaining… high ethical standards.”

Mr Madoff’s lawyer, Dan Horwitz, called his client “a person of integrity” and said he intends to fight the charge. “We will fight to get through this unfortunate set of events.” His client was released on a $10m bond secured by his New York apartment.