iTunes refuses to authorise with my UK iTunes account now that I'm in Ireland
You can have multiple iTunes Store Accounts across different countries or regions. That's not causing the issue for you.

In iTunes, go to the "Store > Authorize This Computer..." menu option and sign in with the UK account to authorize the computer to play content from that store.

If it still does not work (or you have already authorized the computer), then it's likely a temporary error with connecting to the Apple iTunes server.

For more information, see:
iTunes 11 for Windows: Authorize a computer to play iTunes Store purchases