Sir Howard said he recognised that LSE’s reputation had “suffered” after accepting a £1.5million donation from Saif al-Islam, Col Gaddafi’s son.

He said the decision to accept the grant had “backfired” and expressed regret that he had visited Libya to advise the regime. He said it was “a personal error of judgment”.

Speaking on the BBC’s Today programme this morning, Sir Howard admitted making two key mistakes but defended the LSE’s practice of training officials from questionable regimes.

He said it had been wrong to conclude that “it was just about reasonable” to accept the donation and, agreed that working as an economic advisor to the government while being director of the LSE had led to a “muddle”.

But he defended the LSE’s links to Gaddafi’s Libya, saying: “There were no sanctions on dealing with the Libyan regime.

“To say that we will not train officials in developing countries because of what those regimes may or may not do is very curious.”

Pressure on Sir Howard had increased after it emerged that the university agreed to train hundreds of young Libyans to become part of the dictatorship’s future elite. It was disclosed last night that the contract to train the Libyan civil service was worth £2.2m.

The LSE council has commissioned an independent inquiry into the university’s relationship with Libya and the Gaddafi family, to be conducted by Lord Woolf, the former Lord Chief Justice of England and Wales.

The LSE received £300,000 of the donation and has now pledged to spend that on scholarships for north African students.

“I have concluded that it would be right for me to step down even though I know that this will cause difficulty for the institution I have come to love. The short point is that I am responsible for the school’s reputation, and that has suffered,” Sir Howard said in a statement.

“However laudable our intentions, in the light of developments in Libya the consequences have been highly unfortunate, and I must take responsibility for that. I advised the council that it was reasonable to accept the money, and that has turned out to be a mistake.”

Meanwhile in Tripoli, secret police loyal to Col Gaddafi have staged night-time sweeps of the capital, arresting hundreds of opponents and protesters in advance of demonstrations planned for today.

“Several of my friends have been arrested,” said one young man, who cannot be named for his safety. “I do not know where they are. There will still be big protests tomorrow. Inshallah [God willing] Gaddafi will be gone.”

It emerged last night that British authorities had intercepted a ship carrying £100 million worth of Libyan currency and escorted it into Harwich, Essex.

The ship had tried to dock in Tripoli over the weekend but decided it was unsafe and proceeded to Britain, tracked by UK authorities. The seized currency is now subject to UN action. The operation came days after Britain prevented the export of £850million in Libyan bank notes, which were printed in the north of England, to Tripoli.