If you are resident in Ireland and you own a home in the UK you must declare and pay tax on this income in Ireland and the UK.
This is done by submitting income tax returns annually to both the Irish Revenue and HMRC. Of course if you are Irish tax resident, the tax paid in the UK can be used to reduce the tax liability arising on the same income in Ireland. If you are unsure if you are Irish tax resident you should this article here
You should ensure you are registered as a non resident landlord with HRMC.
Why do I have to submit two tax returns annually?
It is a point often omitted by taxpayers but it is important to be aware. Rental income on overseas properties may be taxed both in the country in which the property is situated and in the country of residence of the individual in receipt of the rent. A credit is given against the tax payable in the country of residence, for the tax paid in the other country.
Also watch dividends; these are taxed both in the country in which the recipient individual is resident and in the country of payment, this is the country that the company paying the dividend is resident. An Irish resident individual in respect of UK dividends is taxed on the amount of the net dividend received.
With pensions (other than governmental pension for which Article 18 applies) paid in one country to an individual resident in the other country in consideration of past employment they are taxable only in the country of residence under the agreement.
What will happen after Brexit?
Irish tax residents with UK rental property should read this article to understand the implications after Brexit.
To discuss your personal circumstances in further detail email email@example.com