How's your UK credit history and do you have any available credit there, i.e. overdrafts and credit cards?
In general, in the UK, you can apply for up to 50% of your salary in credit meaning that, on €55,000, you should be able to get a loan of €27,500 (assuming you have no credit cards and overdrafts).
If you have credit cards and overdrafts, reduce the €27,500 by the total limits of these.
With a €27,500 loan in the UK and a €5,000 savings pot, a €32,500 bid might seal the deal with a house with an asking price of €35,000.
This would probably be an easier route than an Irish mortgage and the rates on personal loans in the UK are very competitive, starting as low as 4.8%.