The only 'pattern' to the power cuts is that they seem to take place a
few minutes after switching off my electric shower (note: a few minutes
after, not immediately).

It sounds like the local electricity supply has had a little too much
diversity applied to it. Assuming your shower is at a similar time every
morning, along with everyone else nearby showering and putting on the
kettle, this morning peak may overload the local transformer, which is
cutting out, but auto-reclosing after it has cooled off. Have any nearby
houses been built/newly occupied recently?

Christian.