Therein lies the problem. Even real tax experts don't have straightforward answers for this, and as pilots we are certainly not tax experts. You'd probably need to be qualified as a tax lawyer, accountant and economist to stand a chance of dealing with this correctly yourself.
Your roster should make your home base clear. If your allocated place of work is in Italy and you spend most of your time in Italy then the Italian tax authorities will want their pound of flesh. If your contract is Irish and you work on Irish registered aircraft the Irish Revenue will probably want you to pay tax and PRSI to them. As you are British and have considerable ties to the UK presumably including a house, car, bank accounts etc, the HMRC will probably want you under their jurisdiction.
The whole thing is a mess and a source of stress to pilots. Good luck in your hunt for a straight answer. I don't think your tax and social regime will simply come down to personal choice.