Immigration Act 1968

This Act was introduced to keep out Third World undesirables. Tories & Labour were onside. It was under Harold Wilson, a Labour PM. British nationality law - ex Wiki gives an overall view. It mentions lex sanguinis: the law of blood i.e. by descent.
PS In England there are Superior Rights For Illegal Immigrants

Commonwealth Immigration Act 1968 ex Wiki
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The Commonwealth Immigrants Act 1968 (c. 9) was an Act of the Parliament of the United Kingdom.

The Act amended the Commonwealth Immigrants Act 1962, further modifying rights of citizens of the Commonwealth of Nations countries (now, in 2010, comprising approximately 1.9 billion people, including New Zealand, Australia, The Republic of India, Islamic Republic of Pakistan (which included East Pakistan province), some African nations including Nigeria and many Caribbean islands) to migrate to the UK.

The 1968 Act restricted the future right of entry previously enjoyed by Citizens of the United Kingdom and Colonies, to those born there or who had a least one parent or grand-parent born there. It was introduced amid concerns that up to 200,000 Kenyan Asians fleeing that country's "Africanization" policy, would take up their right to reside in the UK. The bill went through parliament in three days, supported by the leadership of both the governing Labour and main opposition Conservative parties, though opposed by a few Conservatives such as Iain Macleod and Michael Heseltine, and the small parliamentary Liberal Party.[2]

The 1968 Act was superseded by the Immigration Act 1971. The full text of the 1968 Act is online here.
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They can keep Third World undesirables out - if they want.

 

Immigration Act 1971 ex Wiki
QUOTE
The Immigration Act 1971 is an Act of the Parliament of the United Kingdom concerning immigration.

The Act, as with the Commonwealth Immigrants Act 1962, and that of 1968, restricted immigration, especially primary immigration into the UK.

It introduced the concept of patriality or right of abode.
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It was not very effective or not very enforced.