Thanks for the suggestions. I took off the inlet and outlet pipes. No blockages. When the pump was re-priming it sounded fine. Then the noise started again. Hmmm.
So I checked the filter on the tap. And guess what? It was clogged. It's a goofy sort of multi-part filter, and until you take it apart you can't see the gunk in there. But I got it apart and cleaned out. And voilą. The pump runs fine now.
And what possible use is that stupid tap filter for anyway? Sheesh!
It's not the size.....