I suppose back in the day with national flag carriers, British Airways represented the whole of the UK as the national carrier, however as they concentrate on being London centric this may be less applicable now. As always this could also be up for debate being Northern Ireland.
Many, many airlines have their base or head office in England, Scotland has Loganair off the top of my head, ROI has Aer Lingus, Ryanair to name just two; but Wales?? No sizable commercial carrier springs to mind??