Up until the 1960s, all commonwealth citizens could stay in the Britain without any restrictions. The government was concerned about mass immigration and in 1971 it passed the Immigration Act that Commonwealth citizens only had the right to live in the UK if they, their parents or their grandparents were born in the country.
This was in place until today's British Nationality Act was put in place in 1981.
Until this act, commonwealth citizens had the status of "Citizen of the United Kingdom and Colonies" (CUKC). This new act replaced this status with three new categories: British Citizenship (had the right to live in Britain due to close relations), British Dependent Territories Citizenship (had close relations with a colony) and British Overseas Citizenship (everyone else).
Some people also had the British Protected Person status. These were often people from states protected by Britain. They did not have the same rights as citizens.
Today Britain has nationals in six categories: British citizens, British overseas territories citizens, British overseas citizens, British Subjects, British nationals (overseas), and
British protected persons. British citizens are the only nationals with all the rights such as the right to enter and leave Britain freely.
People can become a British citizen by being born in the UK, by descent, by naturalization (immigration) and by registration (for children who have the right to citizenship - must be done by their 18th birthday).