Wow, Barclays need to update their site, saying "A global account for global citizens" is misleading if they insist on a UK address.
Here is another idea, which has worked for posters on other threads; Bank of Ireland in Newry. Here is a link to Bank of Ireland UK's personal current account brochure:
On the last page it says,
"if you are resident outside of the UK, we will request certified copies of documentation to verify your identity and address". This suggests that they will entertain account applications from Irish residents.