If you want to find the catalogue number (eg. P#123), I'd suggest you go to Bank Note Museum, right here:
http://banknote.ws/
Let's say you want to find P#340b under Northern Ireland. Here are the steps:
1) Click on Europe
2) From there, go to Northern Ireland
3) Since your note was issued by Ulster Bank Limited, click on that
4) Find the note that matches yours (
http://banknote.ws/COLLECTION/countries/EUR/NIR/NIR0340.htm)
5) Look at the top left of the page, which says 340. If there are any variants, they are usually listed as ###a, b, c and so on (# being the number), or like ###(1), (2)...
Done!
I hope this helps, and I'd recommend this site for general info on your bills.
Cheers!