stifle is actually correct.

All arrivals in Ireland have to show a passport. The only exception is those arriving from the CTA (common travel area), who only need to be able to prove residence in/nationality of either the UK, Ireland, Isle of Man or Channel Islands. [And naturally enough, the vast majority of passengers will just show a passport as it is the easiest way of accomplishing this]. A boarding pass from a flight arriving from elsewhere in the CTA is not enough - as any nationality may arrive on such flights, and arriving on such flights does not exempt you from having to pass through the passport control.

The Garda you met was most likely being pragmatic and could believe/infer that you were a British national without requiring you to provide proof, but (s)he would have been within rights to ask you to provide proof of nationality.