Q plates are still being issued, mainly to kit cars that are built not using new major parts, such as engine, gearbox, diff.
DVLA will also put a Q plate on a mass produced car if their is a discrepancy in its history, may been imported and paperwork lost.
Good part about Q plate cars is pre ‘74 emmision test at MOT time, only visible smoke test carried out.
Here’s my Q plate Westfield —