Really, it would not be a problem if we didn't elect numpties who tried carrying away open briefcases! It is, after all, a problem no known commercial manufacturer has identified, so must be peculiar to public servants! Now they need to design out the ability to leave any state owned briefcase on a train or taxi seat. Not so good with that one are they :)
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.