A deepening row over the London School of Economics and its dealings with the Gaddafi regime has claimed the career of the university's director.

Sir Howard Davies resigned after fresh revelations that the institution had been involved in a deal worth £2.2m to train hundreds of young Libyans to become part of the country's future elite.

An independent inquiry headed by Lord Woolf, a former lord chief justice, will examine the LSE's relationship with Libya and with Muammar Gaddafi's son Saif al-Islam. It will also establish guidelines for international donations to the university.

Davies said: "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."

His resignation came as a US consultancy admitted mishandling a multimillion dollar contract with Libya to sanitise Gaddafi's reputation in the west. Monitor Group, based in Cambridge, Massachusetts, organised for academics and policymakers from the US and UK to travel to Tripoli to meet the Libyan despot between 2006 and 2008, as part of a $3m (£1.8m) contract.

They included Francis Fukuyama, professor of international political economy at Johns Hopkins University and author of The End of History and The Last Man, as well as Richard Perle, a prominent neocon who advised the Bush presidency on the Middle East.

Monitor said that by arranging for the visits, it had hoped the Gaddafi regime would move closer to the west but "sadly it is now clear that we, along with many others, misjudged that possibility".

The LSE's reputation has taken a battering over links with the Libyan regime, which include a donation of £1.5m from a charitable foundation run by Saif, who studied at the LSE. The donation was used to set up a north Africa research programme. This was suspended last week.

A leaked US diplomatic cable indicates that the British government was also party to the deal to bring 400 Libyans to Britain for leadership training. The cable published by WikiLeaks suggests that other UK universities were involved in similar schemes, though there is no independent confirmation of this.

In an attempt to quell criticism, the LSE said Woolf's inquiry would look at a range of connections with the Gaddafi regime, including:

• The £2.2m contract to train Libyan civil servants and professionals. £1.5m of this money has been received.

• A payment of £20,000 for tuition of the head of the Libyan investment authority.

• A payment to the university of $50,000 after Davies gave advice to Libya's sovereign wealth fund in 2007.

• An award from Gaddafi's charity of £22,857 to cover travel costs for academic speakers to travel to Libya.

Professor David Held, an academic adviser to Saif during his four years at LSE, visited Libya in December 2009 on behalf of the north Africa research programme.

Alia Brahimi, another LSE academic, met Saif in Greece last July to discuss "objectives and expectations" for the programme. Brahimi also visited Libya that month. Woolf will also examine the "academic authenticity" of Saif's doctoral thesis. There are allegations that sections of the doctorate, awarded in 2008, were plagiarised.

The LSE council also noted that when Saif gave a speech at the university last May a protester was allegedly assaulted by one of "Gadaffi's associates". The LSE said the case is currently sub judice.

In September 2009, US diplomats were told by Libya's national economic development board: "The NEDB is cooperating with the UK government and the London School of Economics among other UK institutions on an exchange program to send 400 'future leaders' of Libya for leadership and management training."

A Libyan official told the diplomats that, apparently as part of the same deal: "Two hundred and fifty additional Libyan future leaders would also be trained in Libya.

Likewise, the NEDB is working with universities in the United States (Michigan State and elsewhere), the UK, and France to manage exchange programs for 90 young Libyan diplomats (30 Libyan diplomats are currently being trained in each country)."

The official, Faouzi Saleh Elmozogi, said the NEDB "had also sent 70 Libyan judges to the UK to study English language and international law". The Foreign Office confirmed that the NEDB had sent 70 Libyan judges and 30 diplomats to the LSE to study English language and international law.

A diplomatic source said: "The Foreign Office was aware of the deal. But it was a purely private arrangement and was not something that the Foreign Office was intimately involved with."

Davies, who will stay on until arrangements are made for a successor, admitted making mistakes over the decision to accept Libyan money. He has led the LSE since 2003. "I advised the [LSE] council that it was reasonable to accept the money and that has turned out to be a mistake," he said. "There were risks involved in taking funding from sources associated with Libya and they should have been weighed more heavily in the balance."

"Also, I made a personal error of judgment in accepting the British government's invitation to be an economic envoy and the consequent Libyan invitation to advise their sovereign wealth fund. There was nothing substantive to be ashamed of in that work and I disclosed it fully, but the consequence has been to make it more difficult for me to defend the institution."

The LSE Council will carry out its own investigation into the running of LSE Global Governance, the research centre that accepted the Gaddafi donation. It was established in 1992 by Lord Desai, the Labour peer who examined Saif's thesis.

Peter Sutherland, chair of the LSE Council, said: "Howard has been an outstanding director of the LSE these past eight years and his achievements here will endure long after the current controversy has died away. We accept his resignation with great regret and reluctance but understand that he has taken an honourable course in the best interests of the school."

On Tuesday, the LSE agreed to put £300,000, equivalent to the cash it has received from the Gaddafi Foundation to set up the research programme, into a scholarship for north African students. But that did not end the affair. Instead, the latest revelations put intolerable pressure on Davies, who had begun the week attempting to salvage the LSE's reputation.

He appeared on BBC Radio 4's Today programme to say: "We thought that since he [Saif al-Islam] was not going to control the research that this was a reasonable thing to do and this was supported widely in the school.

"It was debated at some length. We took a risk on that and I think it's right to say that that risk backfired on us.

"I feel embarrassed about it but I don't think the decision was made without due consideration at the time."

The LSE has come under pressure from its students to return the Gaddafi donation. Ashok Kumar, the education officer at LSE's students' union, said: "The recent revelations have shone a light on one part of the relationship between the upper echelons of the LSE and the Gaddafi family, which is deeper and more perverse than we would have ever imagined. This issue is damaging the reputation of the school – it should be a place of learning, not at the centre of unscrupulous dealings with the Libyan regime."