At the height of the British Empire in 1921, the empire covered huge areas of the world and had millions of people under its control. During this time, how easy was it for citizens of the British Empire to move from one part of the empire to another? Was it easy for immigrants from poor territories like India, Nigeria to move to rich territories like Britain, Canada or New Zealand? Or was policy directed towards one-way immigration from rich territories to poor territories?
I can only speak for Canada, but the answer is "no", unless you were a white person who was born in one of those territories.
In 1908, Canada passed a law which outlawed the passage of "persons who in the opinion of the Minister of the Interior did not come from the country of their birth or citizenship by a continuous journey and or through tickets purchased before leaving their country of their birth or nationality"
This was basically a direct outlawing of the immigration of people from the British Raj for a number of reasons:
1: Parts of modern India/Pakistan/Bengladesh wasn't under British rule formally: much of India was ruled by "princely states" so rather than being a British subject leaving from a British port, you'd be a Hyderabadi subject leaving a British port. Aka a no no under this law, even if de facto you were ruled by Britain
2: In those days, ships coming from India basically had to stop at some point before reaching Canada; it was just too far for food stocks and fuel with the technology at the time. Stopping however, even for a bit, would have violated the "continuous journey" part, and therefore they wouldn't have been allowed to land
This is most well known in the Komagatu Maru incident, where mostly Sikh passangers tried to challenge this law by coming to Canada anyway. However, they were forced to return to India, where many were arrested upon return
Also, technically Canada, New Zealand, and Australia were dominions, not territories in the British empire by 1921, and therefore had their own laws on immigration different to Britain.
The 1948 British Nationality Act allowed relatively free movement between colonies and the UK. It basically gave all commonwealth citizens a right to settle in the UK. The numbers able to migrate were limited throughout the 1960's, the right is almost completely non-existent now. This was due to several factors including racism, practical concerns and EU membership.