Well, I thought it was about time I took the vacuum cleaner around, it's about that time of year... so I used it for 5 mins, then got a phone call. After that, Henry would not start.
The problem turned out to be that the brushes, which were very tight in their brass housing. I pulled them out (had to bend up the brass end closure on the housings and pull quite hard on the brush leads), and scrape the sides of the brushes a little with a knife, then put them back in & bend the tabs back).
Normal service resumed. New brushes are only a fiver, but did not need them.