The legal minimum for car tyres is 1.6 mm of tread across the central three quarters of the tyre, all the way round.
In the wet, a tyre near the limit takes noticeably longer to stop than a new one. We suggest changing at around 3 mm, and we mark tyres below that as an advisory on the MOT.
A tread depth gauge costs a few pounds. Or drop in: we check tread and pressures for free while you wait (sample).