Many people say "the United Kingdom" to mean Great Britain.
This sentence is from Korea EFL learners' English reading text book and I think 'be verb' should be placed before to mean because conjunction "that" is omitted after 'say'.
I don't understand the structure
The construction is not acceptable.
If people say that Great Britain is friendly, then Great Britain is said to be friendly.
If some people think that that "the United Kingdom" and "Great Britain" mean the same thing, then that's what you have to say.
You could also say: Some people say "Great Britain" when they mean "the United Kingdom".