Yes Dave, but how do you tell the difference?

You look for evidence that they are illegal immigrants, rather than assume they are here illegally, and throw the burden on them to find evidence that they are here legally.

If someone asked you to prove you were legally entitled to live here, and you couldn't get hold of a UK birth certificate, and didn’t have a passport, are you sure you could do so?
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Bonzo, I'm afraid you haven't actually registered that these people came here legally, as British subjects, born under the Union Jack, just not in the British Isles. They had every legal right to be there, and the British Government has now accepted that this was a giant cock-up.

It's different from what's happening in your countries - though the same kind of attitudes seem to lie behind the policy that's been followed for so many years. Keep Out.