David Edgerton in 'The Rise and Fall of the British Nation: A Twentieth-Century History' argues that the British 'nation-state', as opposed to Britain as a core group of countries at the heart of a global imperial state, was a post-WW2 creation.

One instance of this is that there was no British citizenship until 1948. Until that time, under the law as it stood in the UK (British Nationality and Status of Aliens Act 1914), any subject of the British Crown, including those from the Dominions, was in principle a British Subject and therefore perfectly free to live, work and settle in the UK.

However, it did not always work both ways: some parts of the Empire and Commonwealth had their own immigration laws before then. The British North America Act 1867 gave the Canadian Parliament authority to legislate for 'aliens and naturalisation' in Canada. The Australian Constitution of 1901 also gave the Australian Parliament authority over 'aliens and naturalisation' as well as, more directly, 'emigration and immigration'. So right from the start of the idea of 'self-governing dominions', it was recognised that they could have their own laws about who could move and settle there.

Some of these laws would limit a British Subject from elsewhere in the Empire settling there. For example, Canada passed a series of immigration Acts from 1906 onwards placing limits on who could settle there, and some of these applied to people from other parts of the Empire - particularly if that person happened to be of 'Asiatic descent'.

Canada was also the first part of the Commonwealth (other than Ireland, where 'it's complicated') to create its own citizenship laws in 1946. This led to a Commonwealth agreement on distinct national citizenships in 1947, leading to the UK British Nationality Act 1948 mentioned above.

However, even after the 1948 Act, Commonwealth citizens had freedom of residence in the UK until the passage of the Commonwealth Immigrants Act 1962, and once there Commonwealth citizens had almost all the rights of British citizens, including the right to vote. So until 1962, a Canadian could just get on an ocean liner and sail to the UK, and once there to have the right to live and work there, and to expect to be treated on essentially equal terms as a British citizens.

Australian citizenship was created by the Nationality and Citizenship Act 1948, but citizens of other dominions still had a right to settle in Australia and could become Australian citizens by 'registration' rather than 'naturalisation' (because they were already subject of the Crown).