I get it now. I pop the SIM out and drop it into any old Nokia that allows you to store numbers on the SIM and put a single entry on it called 'My Number'. I'll try that soon!
Duh!
I've found out that the area the phone number needs to be stored in (on the SIM) is 'special' area that O2 don't usually use.
To get a number in there, I need to drop my SIM into a phone that has the functionality to allow the storage of a number into this special area of the SIM.....or some other way of doing it (software, magic key sequences etc).
Eureka! At download.com, I found a lovely bit of software called SIM Manager 2 from a company called Dekart - which works with card readers (which my laptop just happens to have). One download, an old SIM card plastic holder (the thing that you press the actual SIM out of) and some sticky tape, later - I've managed to get the software to read the card.
It shows 3 empty 'Own Number' areas so I added 'My Phone' into one of them, wrote the changes to the card and Bingo! Phone number showing in iPhone. Not synced yet, but now I can't see why this wouldn't work. I am very happy!