I said I'd report back, so here it is.
My self diagnosis was almost certainly wrong, as the podiatrist never mentioned the words "ingrowing toe nail" once.
My problem was on the left foot big toe, with nail growing off to the left, and feeling uncomfortable, potential fungal infection.
She hacked it around further (I had already chopped chunks of it off), and said it was build up of nail pressing into the nail bed. Left hand end of the nail was kinda enlarged. She used a proper industrial looking pair of pincers/pliers/cutter to cut it down. Might try and find something that strong! She smoothed off the ridging on it too, although I'm not sure whether that served anything but a cosmetic purpose. Net result - a substantially cut back and rounded off toe nail, which is feeling far more comfortable now and is unlikely to encounter the ends of my shoes and suffer pressure by that.
I hope that explains it, and sorry if it's too much detail. Cheers. Oh, and I'm pleased it wasn't ingrowing, and doesn't require further treatment although I'd be happy to go back to the podiatrist again if need arises.