A little gem I discovered from Who Goes Home? A Parliamentary Miscellany by Robert Rogers:
The red despatch box is a badge of ministerial office … The lock is on the bottom, not the top, which is intended to ensure that the box is locked before it is carried.
That’s a very smart piece of design, designing out problems at source.
(On a related point: despatch boxes are also available in black, so that they are less conspicuous when someone is travelling with one.)