Just an update: We opted for changing the fuse, which seemed to do the trick. If we renew the lease after this year, I will probably press for a more powerful dehumidifier.
On a side note, apparently some of our problems with damp may be coming from a neighbouring flat. The LL from the flat next to ours came by last week insisting we must have some leaky pipe because the damp in the flat there is really bad. Our pipes aren't even on that wall, and I showed her the shared wall (essentially a hallway, incidentally where we keep our dehumidifier). She admitted the problem is much worse in the flat she owns. I told her that we run the dehumidifier most of the winter. We dry clothes outside or at the laundrette for big loads when possible, crack the windows when cooking, after showering, never dry things on the rads, etc, etc. I suggested the guttering or some other source. But I think it is really think it's because the family that lives in the neighbouring flat. I explained to her that we really take the damp thing seriously, and the dehumidifier basically doubles our electric in the deepest part of winter. I hope if it's structural or the behaviour of her tenants, she can sort it.