Yes, I had a similar situation.
In our experience the mortgage provider added a 25% loading on top of the overseas earnings. What does this mean?
Lets say you earn GBP100k per annum = EUR~117k.
When calaculating your affordability capacity the bank will reduce the EUR117k by 25% so they will consider your earnings as approx ~EUR87.75k.
Your bank may use a different % but that was my experience.
Regarding only needing to borrow half of the Irish property value I would take a look at the interest rate on offer, if it is favourable you may consider borrowing as much as you can for as long as you can & put your capital to work elsewhere potentially earning more than the mortgage interest charges.
I got absolutely slated on here previously for recommmending similar but I stand by it & it's what I'd do if the circumstances are right.
Best of luck.