"David W.E. Roberts" wrote
How do you know when cucmbers and gherkins have finished growing and are
ready to pick?

If they change colour and go soft then it is too late :-)

Yes, by then lots of ripe seed inside. Pick when big enough to use and
before they start to change colour (ripen).

Again, I know that with courgettes you can pick them once they achieve a
minimum size, or let them grow on and they will keep increasing in size.
Does the same apply (within reason) to gherkins and cucumbers?

To a certain extent yes but just like courgettes that are allowed to grow
you end up with something else, a marrow. Best eat them when youngish before
the seeds get too big inside.
Otherwise it's only fit for the compost heap.

--
Regards
Bob

Some photos of my plants at.....