Scotland, Ireland and Wales along with England were all integral parts of the UK with full representation in the UK government. The four nations each benefited from the Union, for the most part anyway. And so with the exception of Ireland, there has never been a majority in any of the four in favour of independence. (that may change soon though.)
Canada, Australia, New Zealand and others were possessions of the UK. They didn't not have representation in the UK government. Instead they had their own system of government headed by a Governed General who represented the Queen. They were, to a great extent, independent from the UK on many matters already prior to official independence. These territories had developed to a level where they could look after their own without the British to assist and so more extensive independence was beneficial to them and freed the British of the costs of maintaining garrisons in far flung corners of the globe. Particularly after WWII when the British were rather strapped for cash.
In addition, post WWII there, the anti-colonial movements were gaining ground and allot of political pressure was placed on the British government to make states independent of them empire (wither they wanted it or not). This anti-colonialism applied to Ireland too as it was seen as a colony, but did not apply to Wales and Scotland, and certainly not the England, as they were, as I said before, integral parts of the UK and closely bonded together with a single government.
Canada, Australia and New Zealand are however still lightly connected to the UK through the British Commonwealth. All the Commonwealth nations share the same Queen as head of state and they each still have a Governor General who represents the Queen in those countries.
Conversely, Ireland left the Commonwealth shortly after gaining independence and so is today completely independent.