David Cameron said Leon Brittan helped transform the UK "for the better" after it emerged that the former Home Secretary has died of cancer at 75.
Last year Lord Brittan was forced to deny accusations he failed to act on a dossier of claims of alleged paedophiles around Westminster.
That row followed a long career which had seen him become the youngest Home Secretary since Sir Winston Churchill and serve as a European Commissioner.
Former cabinet colleague Lord Heseltine said that the peer had been badly affected by being dragged into claims of a cover-up of child abuse - as he hit out at the idea Lord Brittan could have hidden a dossier of allegations.
"I believe he was a man of considerable integrity," he said, adding that there was no way a cabinet minister "can tell someone to lose a document".
"The documents come up the chain. It would have been all over the press within a week."
He said he hoped Lord Brittan's achievements in politics were the measure "by which he will be judged".
Former colleague David Mellor said that Lord Brittan had been sad "after he was subjected to unwarranted criticism and innuendo... It's a terrible way for a tremendous man to go."
The dossier was handed to the then Home Secretary by Tory MP Geoffrey Dickens in 1983.
Last July, amid intense pressure, Lord Brittan confirmed he had been given a file and he had passed it to officials in his department.
But he said: "I do not recall being contacted further about these matters by Home Office officials or by Mr Dickens or by anyone else."
The department later released a letter from Lord Brittan to Mr Dickens in 1984 in which he said the material had been assessed as worth pursuing by prosecutors and was " being passed to the appropriate authorities".
An independent review in 2013 found that Home Office no longer had the documents.
That revelation led to an independent review by NSPCC boss Peter Wanless, who found no evidence of a cover-up.
However, the Wanless report did warn it was impossible to reach any firm conclusions because of the absence of paperwork from the period.
In response the Home Secretary Theresa May commissioned a second, more wide-ranging, inquiry into official handling of abuse claims.
But the proposed chair Fiona Woolf stood down after questions were raised about her links with Lord Brittan, a near neighbour whose house she had visited for dinner.
A barrister who first entered parliament in 1974, in his job as Home Secretary he was dogged by rumours about an alleged sex scandal involving a senior Cabinet minister and under-age boys.
The rumours were denounced as false by the satirical magazine Private Eye, normally the scourge of the political class, which alleged an MI5 plot to force him from office.
After the Home Office Lord Brittan was appointed trade and industry secretary in 1985, but within months was embroiled in the row over helicopter company Westland which eventually led to his resignation and that of then-defence secretary Michael Heseltine.
After leaving government he reportedly rejected a peerage in favour of a job as European commissioner in 1989, and as vice-president from 1989/93 and 1995/99.
But his career in Brussels also ended in resignation, when he and the other members of Jacques Santer's Commission quit amid fraud allegations.
Lord Brittan was made a life peer in 2000 and in more recent years served as a trade adviser to Mr Cameron following the formation of the Coalition Government in 2010.
Deputy Prime Minister Nick Clegg, who worked in Lord Brittan's office at the European Commission before entering politics, said his heart went out to his family "at this very sad time".
His family said there would be a private funeral service for family only as well as a memorial service.
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