Hi,
Whether you should be considered an employee of the UK company is more an issue for the UK company than for you. They are the ones who may have a PAYE or corporation tax exposure, so I wouldn't worry too much about that.
On the basis that you are a self employed contractor you should just ensure that all the Irish tax and social security due under the self assessment system has been paid. If you have reported the income somewhere on the tax return and paid Irish tax on that income then there shouldn't be an underpayment of tax. You may just want to send a quick letter to Revenue confirming that you have noticed that you included the income in an incorrect box on previous returns (although if the correct tax has been paid this may not be necessary, just include it in the correct part of the return going forward). Have you paid Irish social security on the income in previous years? If not there may be an amount due although on 20k it won't be that much. In fact, I'd have to look at threshold amounts but for the last couple of years I don't think the health levy would be due but it would only be the 3% PRSI (would have to check that). PM if you need any help with getting your taxes in order.