Article 7 of the UK/Ireland double tax treaty here states that rental income from a property situated in Ireland may be taxed in Ireland. It is normal for any country to tax rental income on property within its border.
As you are not UK domiciled. you have a choice as to whether you pay UK tax on the Irish rental income as follows:
1 If you remit the income to the UK, it will be taxable in the UK with credit being given for tax paid on the same income in Ireland.
2 If the net income for each of you is less than £2,000 per annum, you can choose to be taxed on the remittance basis without having to make a claim to HMRC in the UK.
3 If the net income for each of you is £2,000 or more, then you can either choose to pay UK tax on it regardless of whether you bring it into the UK (as a UK domiciled individual would have to do) or make a claim for the remittance basis to apply via your UK tax return. If you choose the remittance basis, then you will pay UK on any part of the net rental income you bring into the UK with credit being given for tax paid on the same income in Ireland. Take a look at Section 9 of RDR1 here for information on the remittance basis of assessment.
Once you have been UK tax resident for seven of the previous nine tax years, you will have to pay the remittance basis charge of £30,000 each if you choose to be taxed on the remittance basis for any tax year.
I hope this helps but let me know if you have any further questions.
If the net of expenses income is £2,000 or more for each of you, then you have to choose whether top pay UK tax regardless of whether you bring it into the UK or to pay UK tax on the remittance basis. If you choose the remittance basis for a tax year, you have to tell HMRC. Under the remittance basis of assessment, you would only pay UK tax on any part of the Irish income you remit to the UK in a tax year.