UK Residence and Foreign Capital Gains
If you are resident and domiciled in the UK in the year of sale the HMRC requires you to do a self-assessment return and declare the revenue in the year of sale. The UK government would assess the capital gain for tax purposes but you would get a credit for the Irish Capital Gains tax already paid in Ireland. If the capital gains tax paid in Ireland is more than paid in the UK you would be required to pay any more tax in the UK.
If you are UK resident but not domiciled you will still be expected to do a self-assessment you have the option of claiming the remittance basis which means you only pay UK tax on the income or gains that you bring to the UK. Claiming the remittance basis means you need to pay an annual charge of:
£30k if you have been in the UK for at least 7 of the 9 previous years
£60k if you have been in the UK for at least 12 of the previous 14 tax years
£90k if you have been in the UK for at least 17 of the 20 previous tax years
Regarding your liability to Irish CGT. You will not be liable to Irish CGT if this is deemed to be your principal private residence. There is an allowance in this rule that if you have a period of absence where you are working outside the state these can be treated as the period of occupation.
For this to apply you should be living in the house both before and after the period of absence. You should have no other residence during this time which is eligible for the relief.