I would think the vast majority of books about scroll sawing originate in America, and I think most of those are by Patrick Spielman. I have a couple of books I could recommend by someone called Zachary Taylor who may or may not be British. The books are called 'Success With The Scroll Saw' and ' Scroll Saws: A Workshop Bench Reference.' Both books are from the 1990's so the saws in them are out of date, but the techniques remain very much the same. I don't know of any recent books, but if there are any, hopefully someone will let us know.
I bought good used copies from Amazon and saved a substantial amount on the new price.
Martin.