I know this isn't what you were asking, but please be aware that those British citizens were already living in the UK.
Specifically, they were living in the Falklands, which is part of the UK.
Actually, it isn't - and never has been.
The United Kingdom of Great Britain and Northern Ireland is quite precisely defined - and only includes the three nations (England, Scotland, and Wales) on the island of Great Britain, the northern part of the island of Ireland, and some (but not all) islands in the immediate vicinity of Great Britain and Northern Ireland.
Certain other lands in various locations around the world are considered British territory, but they are not part of the United Kingdom. In 1982, the Falkland Islands were a British Dependent Territory and its residents were British Dependent Territory citizens without necessarily being British citizens (it was possible to be both but a BDT citizen was not automatically a British citizen).
All Falkland Islanders did become full British citizens in 1983, when the British government passed an Act that specifically gave them that status and in 2002, a general act was passed in Britain that gave all British Overseas Territory citizens, full British citizenship) but in 1982, a Falklander Islander might not be a British citizen, and the Falklands have never been incorporated into the UK.
There are a lot of differences between being part of the United Kingdom and being a BDT (the Falklands are now a British Overseas Territory) but as one example, people living in the Falklands are not represented in the Parliament of the United Kingdom. Instead, the Falklands has its own Legislative Assembly, and the Queen appoints a Governor to act in her stead within the islands. It would also be possible for a BOT to be given independence if it wanted it - it would be much more complicated to give independence to part of the United Kingdom.