John Geddes wrote:
A few weeks ago, our consumer unit tripped out at 5am - and it turned
out that a neighbour had had the same happen to them.

Had I been away for a couple of days or longer, I would have come back
to a fridge-freezer full of rotted food.
Msnip
They are suggesting that I should spend money on getting my 7-year-old
consumer unit tested as it must be hyper-sensitive to have tripped out
on such minor provocation.

Should I believe them? What can I do?

Maybe.
I assume that your CU has a earth leakage detector, and that's what's
tripping, rather than anything else.

Depending on the design of this, and the way the network is setup, large
currents flowing in the ground (the large flattish thing the house is built
on, not electrical) can cause the leakage detector to trip.

This is not a fault in the CU - it's working as designed.
It _may_ be a fault with the installation.

Also, current flowing in the ground wire, from the electricity company,
can cause similar problems.