I found it in a spider's web in the house. The discovery coincided with an invasion of bees, but I don't know how long (s)he was there beforehand. (S)he has baffled everybody I have asked.
The best guess anybody has is that it's a hornet but the 'face' looks wrong for a hornet.
There's an ordinary bee in one of the photos for scale.
(While I was waiting for these photos to upload I heard back from a field biologist who doesn't know what it is.)
Do you get hover flies that large?
Looks like you might be onto something with the hoverfly suggestion but it's about twice the size of the biggest one I've been able to find by googling. Unfortunately most sites don't seem to think it's important to give an idea of the size of the bugs they're describing.