Is a UK will valid in Ireland?

Yes, you can have the will made in in England by the English-domiciled testator admitted to probate in Ireland. There are a few tweaks to the usual rules - e.g. to be valid, the English will doesn't have to be in the form, and executed in the form, required by Irish law, so long as it complies with the corresponding requirements of English law. Although the will may nominate an executor who is English-based and that person may have been appointed executor in England, it may be more convenient to have it probated in Ireland (with the consent of the English executor) on the basis that an Irish-based administrator is appointed to deal with the Irish part of the estate.

Irish rules regarding inheritance - e.g. a spouse's legal right - will apply to the Irish assets in the estate. Similarly if there are Irish assets which the will doesn't dispose of, Irish rules will apply to determine who gets them.

If the testator is still alive, he should definitely be taking legal advice (in Ireland) about whether this is the way to go, or whether he would be better off to make a separate Irish will in respect of his Irish estate.