With scales from 1:25k to 1:550k, they’re full of useful tourist information as well as mapping of roads, footpaths, open access areas, and more. | Search by map number or location using our map sheet finder ... The most detailed maps of Great Britain.

The OP is asking for a combination of the 9 England Regions + Scotland, Wales and Northern Ireland, not the country boundaries. Unfortunately, this dataset is not available in the links you shared (you can get the Regions just for England, but not including Wales, Scotland and NI).

Map of United kingdom includes England, Wales, Scotland, and Northerner Ireland; all these regions are shown on the United kingdom region map with their boundaries. However, as you can see on UK map, Northern Ireland is northern part of Ireland island and hence separated from the mainland of other three regions of UK through Irish Sea.

The United Kingdom is situated on the Western Europe map and is surrounded by the Atlantic Ocean, the North Sea, the Irish Sea, and the English Channel. The closest countries on the map of Europe include France, Denmark, and Norway, among others.