You should certianly tax tax advice for this matter on both Irish and UK issues.
If you are a Ltd company and if you do not have an office in the UK, and are concluding all contracts in Ireland, it is likely that you will not have any UK corporation tax issues (but this will depend).
However, if you are personally spending time in the UK, you may be considered tax resident there if you are habitually spending 91 days or more there a year. You need to consider this.
If you become UK resident (as well as Irish resident) you will be dual resident for tax purposes as an individual, and if you are a Ltd company and a director, you may cause the company to become resident in the UK.
If you are self-employed and carry out busines in the UK you are liable to UK tax on the business income arising whether you are UK resident or not.
Other than the above issues, if you do business exceeding a certain amount in the UK you may have to register for VAT in the UK.