Back at the beginning of September I screwed a piece of wood with holes drilled in it over the entrances:
The holes are about 8-9mm in diameter. A mouse could still get in if it really tried, but it seems to be an effective deterrent to wasps, which are wary of narrow tunnels. Note that other people who tried this trick reported no success. I think that’s because they put the entrance reducer on their hives after wasps had learnt there was a bee colony to rob. We had plenty of wasps around in late September, but their scouts rarely ventured into these narrow tunnels.
You don’t want the holes to be too small. If you look closely at the picture you’ll see an undertaker bee dragging a corpse out of the right-most hole. And the holes need to be large enough to push the drones out at the end of Autumn!
I will be leaving these entrance reducers on until Spring. They will reduce draughts. But once the bees begin flying in large numbers, the holes need to revert to full size so there are no traffic jams.