Different iTunes region and App updates I've moved house from the UK to Ireland so now am in a different iTunes region. I have changed store and registered new payment details so I can properly use iTunes again.

BUT, all of my App updates via the iTunes store are blocked. The Apps on the iOS devices themselves are fine and can be updated one by one but not at all through iTunes. 
The Apps I'm interested in are available in both the original and new region App Stores so there should be no licensing issues, particularly since the updates are allowed on the iOS device itself.

Updates to my Mac software through the Mac App Store are also fine now.

Any ideas?
Each account can only be set to one region.  According to the knowledgebase article below, one should be able to change the region on an account.  Since this process doesn't seem to have worked properly in your case, I'd suggest contacting iTunes support.

http://support.apple.com/kb/ht1311

However, you could have two iTunes accounts; a UK account and an Irish account.  The advantage here is that you don't have to worry about a previous UK purchase not being available in the Irish store.

To get an iTunes account in a country in which you do not reside (and therefore do not have an address or credit card from that country), you could purchase an iTunes gift card from the country in question and follow the instructions in the

How to redeem an iTunes Gift Card on a computer > I do not have an iTunes Store account
section of the following knowledgebase article:

http://support.apple.com/kb/ht1574

You will need to authorize both accounts in the Store menu in iTunes.  Once both accounts are authorized, you should be able to update the apps you purchased with your UK account as well as any new apps you purchase with your Irish account.

On your iOS devices, however, you can only be logged in to one iTunes account at a time (Settings app > Store > Apple ID).  On the device, over the air, you can only update the apps associated with the currently logged in account.

I hope this is helpful.