. In England, I've had a purpose-built box on the shed wall for years and never got any interest.
Are they causing problems where they are? If not, I would leave well alone!
No they are not. This has been my feeling all along Hugh, but I don't want idiot neighbour hassling my elderly mum.
Point out to them that bumble bees are endangered and protected. That might shut them up.
I understand that, what might be best is a call to the local beekeepers association. It is likely that they will say "they are bumblebees and not a problem". This information can be conveyed to idiot neighbour which might mollify him somewhat. You can also invite him to remove them if he wishes