I have a domestic built in dishwasher but the door does not shut, the white bit at the top does not close the door,

I think when you say the "bit at the top" you are referring to the metal tab that engages into the door interlock switch mounted in the door frame. If so it is and easy fix.

The metal tab engages the door switch, this is the same switch that is actuated by moving the handle on the door. It tells the machine that the door is closed and it is OK to start. The tab can become misaligned or bent over time and will not engage properly.

To fix this the easy way is to simply bend the metal tab so as it engages properly. You will need to fiddle with it to get it to the correct position but it will work when you get it there.

The only other door jam that can happen is the springs the support the door become jammed. This you will know right away if the door just falls to the floor when opened. The springs can jam in the door hinge and stop it closing. You would pull the machine out and reconnect the springs. But from what you say this is not the problem.

I hope this help you, please take the time to rate this answer.