I think the answer to this question is that both the Saxon and Norman rulers of England, as well as the Plantagenets, tried to dominate the British Isles in one way or another.

Many of the Saxon Kings, such as Athelstan and later Edgar, claimed the title 'rex totius britanniae' or King of all Britain, with homage paid to them by Welsh, Scottish and Irish Lords.

This claim was later invoked by Edward 1st with his conquest on Wales and attempted conquest of Scotland. R. R. Davies covers this brilliantly in his book 'The First English Empire'