Thanks plyphon.
I got the Cape Cod polishing cloths that neilnevill suggested, and they made a big difference. You can still see the scratch if you know where to look, but there’s no sharp edge on it now, so nothing to catch the light and make it noticeable.
Should probably have popped back to update before, but there you go, and thanks for the suggestions.
I heartily agree with you about wearing them daily, but I’m probably going to be a little more thoughtful about where in future. I bashed it on pipe coupling when undoing a nut on one of the Gas Turbines at work.