Point of information: "Celtic" is not an ethnicity. It will not, therefore, show up in anyone's DNA. "Celtic" is a language group and the latest archaeological discussion I heard said that they now think it was a trading language, which accounts for how widespread the language finds are across a lot of Europe, but particularly on the trade routes.
"British" is a term open to much misunderstanding as well. There's the historic version and the modern political version.
The "Iberian" origin has been much talked about here in Wales as well as elsewhere to account for darker skin tones and black curly hair. There is very unlikely to be a clear "British" DNA marker, given the various groups of invaders and settlers across the whole archipelago.

But good luck with finding out your family history - I'd love to find out more about mine but there's a missing great-grandfather complicating my mother's side of the story.

Anne