The university has also revealed that it had signed a 2.2 million pound contract with Libya to train its civil service and had already received 1.5 million pounds of that from the dictator's regime.
The university has announced that former Lord Chief Justice, Lord Woolf, would conduct an independent inquiry into the university's link with the Muammar Gaddafi regime, The Daily Mail reports.
In a statement, Sir Howard said: "The short point is that I am responsible for the school's reputation, and that has suffered. I advised the council that it was reasonable to accept the money and that has turned out to be a mistake. 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," he added.
The university came under huge criticism after it was revealed that Gaddafi's son, Saif el-Islam Gaddafi, had paid 1.5 million pounds as donation to the institution, which was made a year after he was awarded a doctorate by the prestigious institution. There have been allegations that Saif's work was plagiaristic in content.
Sir Howard, a former head of the Financial Services Authority and deputy governor of the Bank of England, would however, remain as the head of LSE until a successor isfound.