Thanks for all the suggestions, and my apologies for not following various comments up sooner. Unfortunately, as I said, the problem isn't the usual muck and gunge. It's bits of grit, and what sometimes looks like flakes of paper which have wedged themselves in the grooves over the years.

Unfortunately, I can't afford a record washer. But a combination of permaclean and carbon fibre gizmo sounds as though it might do the trick.

I've just checked on-line and Maplin have carbon fibre cleaners in stock at £9.99.