I couldn't find an affordable replacement Brake Light Switch, so tried one for a Mazda MX5, of which there are quite a few available. It fits perfectly.
Thanks to 0114campervan on e-bay (based just up the road from Bongo Fury HQ), I now have working break-lights again.

Thank you all for you replies. It was the rear propshaft after all. One of the universal joints had seized. This fooled our mechanic, because it wasn't loose as it would have been if the joint was falling apart. He told me that he has learnt something (which I think must be quite an achievement with ...

Our Bongo is making a worrying noise and we have had no luck with our mechanic figuring out what it is, so we thought we'd describe it and see if anyone has any ideas.

It happens during acceleration, especially when pulling out from a stop, and is more pronounced the harder the accelerator is ...