The stall warner should go off several knots above the stall, so there was some margin. However that's closer to stall than I would want to be on turning downwind to base. Usually it's the base to final turn which is the slow, dangerous one. Did it go off again on the flare out?
Also bear in mind that the stall warner may not be very accurate in an old aircraft. Our's isn't - it can go off within a 15 knot range of true stall speed. In fact we have silenced it temporarily until we can get it more reliable.