We're thinking about replacing a tastless old gasfire with a woodburner.
The chap in the fireplace shop said that the chimney wouldn't
necessarily need lining if it had been in regular use with either an
open or gas fire, and that they'd do a smoke test to see if it did.

Is that correct? Is that all you need to do to check that a chimney is
sound? It's a 1930's house, BTW.