Sorry if those of you on the West Coast were just woken up by the shout of "YES!" from Sheffield UK. This was me finding that the ends of my binding were perfectly joined together. Thankyou to everyone who's contributed to this thread. I used a method in a tutorial here on the board that Kitsie very kindly pointed out to me.
http://www.quiltingboard.com/t-51632-1.htm
But I'm likely to have several more binding jobs in the near future as I quilt my ufos (at last!), and it'll be interesting to look at some of the other resources that have been suggested.
Incidentally, it's the quilt in my avatar that I'm working on. I've used stitch-in-the-ditch, which looks great on a plain brown backing fabric.