The car in question is a 2012 VW Polo. I had last driven it 4 days earlier on country A-roads for about 75 miles there and 75 miles back. Then today after I left the house and had driven about 100m on the lane at about 20-25mph, I suddenly started hearing a high-pitched scraping noise.
I got out and determined there was nothing hanging off the bottom, and nothing I could see in the wheels. The scraping sounded very similar to the noise in this YouTube video.
I drove less than 100m more and the noise disappeared, then came back after another ~100m when I got to the end of the lane. As I joined the slightly faster main road, the noise disappeared again, this time for the whole of my 12 mile round trip.
The noise only occurred when the car was moving, and did not intensify when I braked. I couldn't tell which wheel it was coming from.
I'm thinking it might be due to a stone that got temporarily lodged somewhere, as this YouTube video explains.