Does anyone have experience of tracking down stuff like this ? Is it
worth
turning off the consumer unit and doing the N1-N2, L1-L2 tests mentioned
in
the FAQ ?

You've probably got an earth-neutral short somewhere or such like. These can
cause weird trips even of different circuits. You should do a full periodic
inspection, which should hopefully find which circuit is at fault, which
could be completely different from what you are expecting.

To do the tests you need a proper continuity insulation tester. A 6 quid
multimeter from Maplins will NOT suffice.

Christian.