Can someone be Great British?

No. Historically Great Britain refers the larger territory ( the British Isles), Lesser Britain was Brittany. The people of Brittany do not call themselves British. Therefore anyone from Great Britain is just British.

Um... Scots are Brits.

Kind of like I'm Virginian, but also American.

No. The correct term is British. Great British is ridiculous. You also need to ask this in the Languages forum. This is the Royalty forum. Use the edit feature to recategorise your question.

The English, Welsh, Scots, and Northern Irish are all British.

Hello everyone,

I've heard people referr to Scottish people as British before. For instance to David Tennant in the Red Nose Day special of Katherine Tate. As far as I know, British only referrs to England and Wales, where Great Britain includes Britain plus Scottland. So the correct term for a Scotch person like Tennant wouldn't be British, it would be Great British. I do assume saying British simplifies it and people do it to keep it simple, yet I have never heard anyone using Great British, so Great Britain as an adjective and whenever I used it in my mind it just sounds wrong. So I thought I'd just ask some native it something like that would ever leave your tongue naturally.

Margaret Thatcher was.