Another possible briticism from the book I'm reading:

"We did it!" Jelly said. "Thank gordon."

[And later, Flick speaking to Jelly:] "Don't let the Nazis capture you alive." "Oh, my gordon," said Jelly.

Meaning 'thank god' and 'oh, my god'? How did this come about?

I've never heard it. Is it authentically British? In other words what nationality is the author?

Or is it perhaps meant to be an idiosyncracy of the speech of that particular character?

I've never heard it, either. It might be that particular writer's (or character's) euphemism for "Oh my Gawd!" (God).

Per your questions. The book is Jackdaws by Ken Follett. Follett is British, and seems to research his books thoroughly.

We meet the Jelly character in a pub named The White Swan (but commonly known as The Mucky Duck) in London, specifically in "Stepney, not far from the docks," and we're told that she grew up in that neighborhood. She's the only character who grew up there; she's the only character who uses "gordon" this way, and she uses it consistently.

So I suspect it's local slang in the area, or in-the-area-at-that-time.

"Gawd" is is a common cockney (or more properly east London) pronunciation of "God". At a guess it's a minced version of that, possibly of the character's own invention. There is also another oath "Gordon Bennett!", an alternative of "Gor blimey!", which is itself a variation on "God blind me!".

See also http://www.peevish.co.uk/slang/articles/gordon-bennett.htm