Thanks to Dick Pountain for reminding me that the bleedin' obvious isn't always.
I was groping around for a desktop search program that could look into any file, not just some standard list of extensions such as those handled by Microsoft's search. I looked at loads of programs and even downloaded a few but none did what I really wanted: to index a bunch of largely text files with the .brn suffix. In fact I didn't even need them indexed as long as I could search inside them reasonably quickly.
As a web developer and occasional programmer of many years' standing, I'd been using TextPad as my editor of choice. And, when I wanted to do global edits, I'd use its 'find in files' function. It just never occurred to me to use it to look inside other files. Until Dick suggested it.
Now, I set the file type to *.brn, the root of the search to 'desktop', tell it to look in sub-folders and the search to whatever I'm looking for. With regular expressions if I'm feeling flashy. Bingo.
As a paid-up user, why didn't I think of it before? So simple, so quick. Thanks Dick.