Wow, thanks for all the good replies. I spent last night experimenting with loading of the film, and I think you're right that that has been the problem. I wasn't aware of the trick of looking at the rewind button (but I am now, so thank you ;-)). I tried loading another film and saw that the rewind button wasn't turning when I took pictures, so I tried again loading the film, and this time it did turn!
Thanks again for all the replies, it has helped A LOT.