George Orwell was born in India at a time when it was still part of the British Empire, so technically not an immigrant. No idea where JL was born but presumably that would also have been during the empire.
I think military bases also have a slightly different legal status (like embassies).
Otherwise, yep of course people born overseas who move here later in life are immigrants. Depending on the two countries, they may not be entitled to a passport in their parents’ home country, and often wouldn’t be able to pass on citizenship to their own children. Which is why many people decide to go back to their original country to give birth.
If you think they aren’t immigrants, does that mean that people born to eg Indian parents here are still Indian and not British? Because I’d say they are definitely British.