Chris H's answer pretty much nailed it, but I'd like to add an answer to capture useful points made in the comments.
The job turned out to be really simple and the only tools needed were an allen key and a piece of old pipe. I tried getting penetrating oil into the bush without taking off the arm, but after two days it had little effect so I had to take the arm off.
As Chris said, the bolt was really, really tight. In the end I put a piece of pipe over the end of the allen key and the extra leverage did the trick. Getting the arm off the pivot was a bit hard, but I just wiggled it to and fro whilst pulling for about five minutes and it eventually came off. It didn't any great force, just a lot of patience.
On my bike the spring is secured to the back of the arm so nothing dropped off or came apart when I took the arm off.
Compton warned me to check which of the three holes the spring was attached to, but of course the spring came free before I could check. However it was obvious which hole the pin on the spring needed to go in as trying the other two holes made the spring tension obviously wrong.
And that's all there was to it. I rubbed the pivot clean with some wire wool. I didn't have a tool to get at the inside of the bush in the arm so I just pulled a cloth through it to clean it as much as I could. I put a small amount of lithium grease on the pivot, refitted them and it now works perfectly.