At the risk of stirring up this thread again....
I've just found a queen wasp and the beginnings of her nest (about the size of a walnut) in my shed.
So, what do I do? Kill or leave alone?
Exactly the same in my garden - in the bee shed, cheeky blighters, about 6' from the hives. Again, about walnut-sized.
I don't normally bother to kill wasps because there's just so many nests about (e.g. in the banks of the adjacent railway line, and neighbours' gardens esp. under decking) that it doesn't make a huge difference. Plus, they have their place, eating pests and clearing up dead bees from around the apiary. The big yellow queen wasps are rather magnificent in their own way. And the hanging nests are real works of art. So I'm probably up the more tolerant end of the spectrum of beekeeper tolerance!
However, when it comes to going in and out of the shed without major stinging (the door would dislodge the nest slightly every time I went in) then I get a bit more ruthless. There was only the queen in there, so I sprayed it with WD40 this evening, including the entrance to discourage any further nesting attempts.
A nicer way of doing things is to wait until evening when the wasps are quiet and in the nest, then quickly knock the whole thing into a binbag, tie it up firmly and simply take it elsewhere, preferably whilst still wearing a bee suit in case of reprisals. I did this with a beautiful round nest a few years ago that was causing a problem in my neighbour's attic. Neither of us wanted to destroy it, so I took it out into some woodland nearby and quickly shook the nest into a dense pile of dead wood that no-one was likely to want to disturb. We sneaked back there the following weekend and found that they had papered the nest onto one of the logs and just carried on.