Does anyone own one they can recommend, or NOT recommend?
Budget is around £150-£200. I am
particularly suspicious of the 30-35-40mm figures they give for acceptable
thickness.

We have a Champion quiet shredder from Focus and are very pleased with
it . It copes easily with 40mm fresh branches. A couple of years ago
when we bought it, it was about £250 and a Which? best buy - rated
better than the more expensive but similarly specced Bosch/Atco model.
It's made by Atika in Germany:

http://www.atika.de/

Look for Gartenhacksler. The Atika impact models (ie. not the quiet
ones) were also Which? best buys at the time.

As well as making the Champion models for Focus, they also sell them
in the UK under the name BioLine, but I seem to recall they were more
expensive under the original name.