OK... here is my very rough attempt.
Have the Conservatives win the 1945 election, led by imperialism's most passionate supporter Churchill. Somehow, Churchill realises that India will have to go for the good of the wider empire, but the withdrawal of the British from the subcontinent takes a much more leisurely pace, giving citizens of the Raj more time to move around to their new homes. Riots do take place, but these are swiftly subdued by the British, who are now essentially peacekeepers in India. The country gains full independence in 1952, divided into India, Burma and Pakistan with the British maintaining a naval base at Calcutta, and full control over Ceylon.
In Palestine, the British realise that maintaining control over the mandate is futile and pointless, and they pull out almost immediatly. This leads to a short, violent civil war in the area, but with ultimately few British casualties.
In 1955, Communist revolts break out across the Empire. Though the Labour government is initially unconcerned with the maintaining the colonies, President Eisenhower realises that to allow Communism a free hand in Africa and SE Asia would be to invite disaster, having already seen the mess French Indochina has fallen into. Large loans are sent to the Colonial Office to fund putting down these revolts, which, by around 1960 has largely been done successfully.
Aided by the empire, British economic recovery comes much more quickly. Harold Wilson's government (1965-1973) realises that if the support of America is to be assured, then the empire must be conserved as a great power. Labour begins to show more and more support to the development of the colonies. As British heavy industry begins to slow down, it is simply moved, piecemeal, to Sub-Saharan Africa. In 1970, Wilson introduces full "Citizenship of the British Empire" to anyone in Britain or the colonies, promoting travel between them. As the empire is brought closer together, so the people begin to see each other as equals. The popularity of Elizabeth II does this, as does the vast flow of young people, both natives to the universities of Britain, and British to "backpack the Empire" as becomes popular in the 1970's. During this period, the British, this time under Keith Joseph's Conservatives (1973-1977) begin to introduce more and more self governance and autonomy within the colonies.
Hmm this keeps the empire going until 1980... But is it very ASB?