A 40mph head on collision would set the airbags off, there is no doubt about that. From what you're saying, it sounds very much like the airbag or the sensor is faulty, which is an MOT fail at the best, death at the worst.
If it's an older car, it's entirely possible the CO2 canister that inflates the airbag has leaked or gone wrong in some way, the material for the airbag has degraded to the point where it no longer works or, and most probably, the sensor in the front of the car has gone to Silicon Heaven