I do not think the the varied and diverse negotiations the British engaged with various Imperial members compares to the Scottish issue because no colony ever entered into a political union with England. No colony ever sent MPs to Westminister, no colony was ever legally part of the "United Kingdom." It is Scotland and Ireland's political union with England that made them unique within the Empire.

But to answer the rest your question, the answer is simply it varies. Some colonies had very violent nationalist movements and it took decades of conflict to resolve the issue. Some colonies became independant very gradually through a series of amicable agreements. Some had a mix. Some became very independant very quickly and were not prepared, for some independance was so gradual that it is a serious academic debate when it actually happened.

If I had to generalize I would say there three templates that the British used: CANAUNZ(SA), Rest of World, and Africa.

For Canada, Australia, New Zealand, and South Africa the British and the nationalists tried roughly the same scheme - a series of peaceful and amicable negotiations. For Canada, Australia and New Zealand the process went very very smoothly - so smooth it is unclear when these nations became legally independant of the UK. The World Wars were a huge influence as Britain essentially traded rule of these colonies for security assurances. Britain tried similar routes with South Africa however due to internal tensions within the colony it was less successful. South Africa sought independance much more aggressively and unilaterally.

The Caribean is a transition point between CANAUSNZ(SA) and Rest of the World. The minority white populations were given self-rule in the mid 19th century and looked like they were on the CANAUSNZ track. However the crash of the sugar economy, combined with white fears of majority rule meant the white populations clung to London. As a result it took peaceful nationalist movements similar to Rest of World grass roots organizations to achieve an amicable separation in the 1960s.

The Rest of the World experience is best summed by the Indian subcontinent but also includes Guyana, Burma, Kenya, and Egypt and several other places.

The basic template is that a non-caucasian population, led by charsimatic leaders, organizes itself to oppose through a mix of violence and non-violence British rule, starting in the early 20th century. In exchange for loyality during the WW1 the British make alot of noise of a new constitutional arrangement. Throughout the 1920s and 1930s the nationalists use violence and protest to try to hold the British to their WW1 deal. With the arrival of WW2 the British cut a similar deal and it is, for the most part, accepted. However, unlike after WW1, the British, to varying degrees, hold up their end of the bargian and make peace with the nationlists. The process is not smooth nor easy and at times very very violent. But by 1960 all these states are independant and have a relatively friendly relationship with the UK.

Africa is its own experience. Like the Rest of the World, much of Africa had nationlist movements led by strong leaders violently and peacefully oppsing British rule. The movements however started later and have their own intellectual tradition separate from groups like the INC. The British started to leave Africa in 1957, with Ghana. What separates the African experience from the rest of the empire is the speed with which the British left - they were out of everywhere except Zimbabwe (Rhodesia) by 1968. The British struck quick deals and left, at times with very troubling consequences.

Now there are exceptions to every one of the things I said. Newfoundland and the United States of America break every rule in the book for CANAUSNZ states, Cyprus, Singapore, Malta, Nepal, and much of the middle east also are hard to group. Rhodesia has its own totally unique experience. Diversity of nation, experience, and agreements is a fundamental characteristic of the British Empire.

Source: Canadian History Undergrad, a undergrad course on British Empire 1856-1956 as well as Stanley Walport's A New History of India

The ones that spring to mind are India and Pakistan and their negotiations were carried on in the very early days of WWII.

India had gained a certain level of autonomy and a legislative council formed under the Government of India Act 1919. Israel was formed post WWII as was Jordan.

The "White Dominions" were different.

Scotland, well it wasn't really a colony , more like a junior partner in the empire business. The Unionists in Northern Ireland are of Scottish descent from a very Scottish Plantation of Ulster.

Pre David Cameron, his two immediate predecessors , Brown and Blair, are Scottish.

Which brings me neatly on to Scottish Imperialism which is conveniently forgotten at the moment.