Following the War, Britain made it an objective to give India independence, however it was much harder for the African colonies and included armed resistance? (Kenya, Rhodesia,etc..)
In a short answer - Haileybury School!
In a longer answer India presented the perfect storm of a well organised independence movement, relatively weak 'Indian lobby' or romanticism of the Raj by 1945, WW2 and an expert and sympathetic PM with economic circumstances to force the hand.
Attlee
Clement Attlee was the incoming PM in 1945, social democrat more than socialist the leadership-by-committee Attlee had always been informed about Indian issues. He was educated at Haileybury College, the de facto school of the Indian Civil Service (first by the fact of its lower-public school reputation/East India Company founders and then almost by tradition). Attlee's technocratic instincts were at full pelt when he staffed the Simon Commission on India (1927-1930) and by all accounts he immersed himself in the Indian question well beyond the casual assured imperialism of the likes of Churchill. Throughout he increasingly believed, along his soft-anti-imperialist social-democratic lens, that Indian decolonization was an inevitability which was better to be managed rather than fought and lost. Ever practical and left wing, Attlee was relatively immune from the romanticism of empire and emboldened by the technocrat's grasp of the complexities. He was, as we shall see, a formidable force in pushing the issue of India from the backburner to rapid decolonisation
Pushing at an open door
The strength of the movement combined with the relative sympathy India commanded on the left had meant that even before 1945 India was moving towards self government. The Montagu-Chelmsford reform of 1919, the Indian Government Act 1935 and Cripps' failed mission in 1942 all advanced notions of Indian independence with escalating resignation though somewhat foundered on the Muslim-Hindu question. At the centre of all of this was an awareness that Britain could not effectively repress millions of Indians and keep the benign liberal-imperialism which sustained the colonial classes - something even Churchill seemed to understand in his lucid moments. Indeed the relatively conservative Viceroy of India in 1944 Wavell pointed out that post-war Britain's reputation would "stand or fall" over India in the post war period. A reluctant march towards home-rule, best epitomized by Baldwin's and Ramsey's desperate wheeler-dealering towards the 1935 act, was the order of the day well before 1945.
The lack of an Indian Lobby
Key to this, without being overly comparative, is that throughout this process there was not a vocal or impressive Indian lobby. This generally makes things easier politically and avoid the kind of posturing which distracts from rational twilight-colonial decision making (as did the relative lack of violence directed at British representatives which, if in occurrence tends to give opposition ammunition and harden public opinion thus a government's room for scope). Indeed the whole retreat from India was dealt with, by and large, in a matter of fact way by the British as a whole. It is fairly convincingly argued that this is in part due to the fact that the withdrawal from India had been anticipated for decades. The Montagu-Chelmsford reform of 1919 are argued as a signal of the beginning of the end however in may ways it can even be traced to the upsurge of the Indian National Congress and when it spilled onto British newspapers in the pre-war period. Britons had decades of increasingly resigned debates to come to terms with the need for Indian independence and the impossibility of governing a reluctant population hundreds of millions large. Additionally the continued cultural, economic and international ties which carried on throughout the 40's and 50's acted as a cover/security blanket and for some even pointed to a new post-imperialist order which preserved much of the advantages of the old world at a fraction of the political and economic cost. There are obvious exceptions, such as the Beaverbrook press and Churchill, however in the post war brave new world of New Jerusalem the imperialist rhetoric and glory counted for less and if anything arguments of a new world order different from the old, forward facing and collegiate carried more, if certainly not total, weight.
Towards a solution
Attlee was sympathetic, the battle was already being lost in the minds of Indians and Britons and the British had elected Attlee on a mandate for domestic improvements and welfare not on an Churchillian Great Britannia. WW2 was a profoundly humbling experience for Britain and its imperialist pretensions which further allowed the emotional disengagement from the Raj for the majority of Britons. In reality should there have been a PM who ideologically opposed to decolonization it could have been forestalled but under Attlee the political and economic reality meant that pragmatic realpolitik was the order of the day. From 1945/6 onwards the question was not really if but how. The primary concerns were:
It had to be done in a way that kept the commonwealth influence there
The thorny issue of the Muslim/Hindu divide had to be resolved to ensure chaos would not fill the void of the British exit. This was vividly escalating as shown by the 'Day of direct action on 19/8/46 which claimed 5000 lives and sent the Labour 'fixers scurrying across the world to find a solution.
To this end Mountbatten, after a brief interference by Wavell, was appointed with broad powers and a remit to sort the issue, an appointment which was followed by the technocrat Attlee's missives. Attlee had all by decided that partition was required after Labour's go-to stern firefighter Cripps foundered on the Muslim/Hindu split in his adventure in 1942. This acceptance sped up the process and it was only a matter of months before this was advocated from number 10 with gutso. After a rather hurried withdrawal as part of a semi-game theory style diplomacy between Mountbatten and the Muslim/Hindu representatives in order to break the deadlock 300 years of the Raj was hastily and somewhat unceremoniously brought to an end.
In all therefore the Indian experience owed its relatively easy decolonization was a constellation of factors. A well organised and relatively sympathetic independence movement mixed with an unpractical-to-repress large imperial possession led to a disengagement well before final independence, easing the process for all. Central to this, and critical to get the impetus moving was Attlee as PM, informed, practical, sympathetic and with far bigger goals and problems at home he was perfect to move Indian independence to its logical conclusion. It not an accident that many later examples of decolonization were slowed or frustrated by Churchill's return to office in 1951 or by the intransigence of the various expat lobbies and/or the disorganized violence hardening government resolve and providing easy wins of anti-decolonization lobbies. This is where many other decolonization movements fell down - though it is important to ensure a sense of perspective of the British experience when compared to the French.
Sources
Porter The Lions Share ISBN 0582089433
Darwin The Empire Project ISBN 9780521317894
Morris Farewell to the Trumpets ISBN 9780571290703
Morgan Britain Since 1945 ISBN 9780192802255
Was the desire to hold on to African colonies a Reaction to the lost of India?
Was it much harder? Apart from the Mau Mau terrorism in Kenya, what armed resistance? What violence?