Erm, don't think it is to do with the button in the door shut - that just controls the lights.
The central locking servo in each door has both the ability to lock and unlock the door, and also a sensor to tell the control mechanism what position the door pin is in. When the car was made (before remote control plippers), you would put the key in the drivers door and unlock it. Moving the pin up with the key would signal to the control unit that the door was opened and it would then open the passenger side. It would also move the pin up on the drivers' door, so if you didn't move the key that quickly then you would feel it kick slightly.
What I suspect you have is a wiring problem (probably a wire gone to ground - poor insulation) or a fault in the servo in the drivers door. Get a wiring diagram (www.cannell.co.uk) and work out what colour the wires are and what they do, and take the door apart and test 'em with a multimeter. The fault will be pretty easy to find, I'd have thought, and cheap to fix. (Servo motors can be bought in Maplin for about £7.)
Oli.