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Mr Gaitskell, who was 56, died at 2120 this evening in the Middlesex hospital in Marylebone. His wife, Dora, was at his bedside.
A short statement issued to journalists after his death said, "Mr Gaitskell's heart condition deteriorated suddenly and he died peacefully".
Shortly afterwards the Queen sent a message to Mrs Gaitskell expressing her "deep distress".
Tremendous fight for life
Other messages of sympathy came from former Prime Minister, Sir Winston Churchill, former Labour leader Earl Attlee, US President John F Kennedy and other world leaders.
The Gaitskells' two daughters, Cressida and Julia, were summoned to his bedside after the news of his death had been broken to them.
John Harris, Labour Party official spokesman, said doctors told him Mr Gaitskell had put up a "tremendous fight for life" and had shown "quite extraordinary courage".
Mr Gaitskell became ill with flu in mid-December. A medical check-up showed he was fit to travel to the USSR on 1 January for talks with Soviet leader Nikita Khrushchev and he appeared well over Christmas.
But immediately after the holiday he became ill with another virus and was admitted to hospital on 4 January.
Two days ago his condition deteriorated suddenly and it became clear his kidneys had been affected.
The night before his death, doctors attempted to treat Mr Gaitskell using a kidney dialysis machine.
A total of nine doctors and 40 other medical staff were involved in the operation to link up his body to the machine.
Although initial results suggested there was some improvement in his condition, it was later felt the machine was putting too much strain on his already-weakened heart and he had to be taken off it again.
His death comes as Labour appears poised for victory at the next election thanks largely to Mr Gaitskell's efforts to make the party "relevant and realistic".
His rise to leadership of the party just 10 years after entering Parliament was one of the most spectacular in modern political history.
Hugh Gaitskell died of lupus disease - a rare and potentially fatal condition which can affect any organ in the body.
Tributes were paid to his first-class intellect, integrity, great courage and to the prime minister Britain never had.
As Chancellor of the Exchequer he introduced charges for spectacles and dentures to pay for rearmament - a move fiercely opposed by then Health Secretary Aneurin Bevan.
During his time as Labour leader, he tried to modernise the party by ditching Clause Four (common ownership of the means of production) but his proposal was rejected.
He fought a second internal battle over the party's defence policy. In one of his best known speeches he pledged to "fight, fight and fight again" to make the party change its mind over support for unilateral nuclear disarmament and he succeeded.
Harold Wilson won the party leadership and went on to lead Labour to general election victory in 1964.
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