Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
If you spend 183 days in the UK in any one tax year you are liable to UK taxation on your world wide income. Under the Double Taxation Convention between the UK and Ireland the same income stream can only be taxed in one jurisdiction. This is achieved by means of tax credits, the tax paid in one country being allowed as a tax credit against any liability in the other. The Convention does not, however, protect you from differences in rates of taxation.
I do hope that I have shed some light on your situation.
Thank you for your excellent support.