I have 24mm rims – can I use 23mm tyres? Or do I need to stay bigger than the rim width – ie 25mm?

http://sheldonbrown.com/tire-sizing.html

Look at the table about 3/4 of the way down the page.

1:1.4 is preferable. 34c would be the minimum reccomended.

24mm is that internal?

It’ll work fine.

Whoops I made a typo. They are nominal 20.5 and ETRTO 15 – Fulcrum racing 5’s…..

So I use the 15 on Sheldon’s chart (thanks imnotverygood), which gives me from 23 to 32 – right?

Yep you can run 23s on racing 5s.

I’ve got either 23 or 25s on my A319s too and haven’t died yet…