2001 Vauxhall Vectra severed rubber pipe which had been rubbed through on the cam belt

I think I know the pipe you mean, is it about 5mm in diameter? Its the vent pipe from the carbon fuel tank vent canister. Easily available from H**f**ds. If its not this pipe let me know what sort of size it is.
Doesnt usually stop the engine, just makes it run roughly.Likewise doesnt affect the remote locking. Try re-aligning the key fob (assuming its the original Vauxhall 'teardrop' or key type) to the car. Open door with the key , insert key into ignition and press the lock button and hold it until the door locks in a few seconds. Unless the fob is faulty or the fob battery is flat it should now work.
Drew