The path of least resistance being the plastic bit that stuffs into the steel handlebars, I took a knife to that instead, slicing off bits that seemed excessive, et voila, it fitted.
Round the block, over some (aren't they all?) bumpy N London roads, and result, excellent. Top Mirror, the Blackburn. Vibration-free, good rear image, far enough out to miss your elbow. Really pleased with that, thanks Dave!
I might even do the same on the nearside, as the other advantage of that particular mirror is that you can bend it right in to 90° to stop it getting in the way in sheds, hallways, etc.
Thanks again for the tip.
Allen.