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I've unintentionally left a cut tile overhanging by about 3mm. As the tile is well stuck down, I have to reduce the surplus in situ. Should I try a tile file or a tile saw, neither of which I have at the moment, though they are quite cheap. I don't fancy scribing and nibbling, nor using an angle grinder.

I can post a picture if needed.

You seem to have covered all the bases in your post. Tile files and tile saws are not up to that kind of job.

Make it easy on yourself and take the tile off then cuta new one. you will have a better day of it.

Taking the tile off is a daunting prospect, it's on unskimmed plasterboard, but I'll leave it until later. The alternative is to leave it, and put extra adhesive under the other tiles.

Score the paper around the tileand then peel the whole section off. Repair it with bonding compound or cove adhesive before you retile.

That should take you about ten minutes. I understand your point though. I HATE going backwards.

In the end, I left the overhang, fixed the tile corner beads, and though the grout lines will be wider in one place, it won't look too bad.