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Brian, the Scots and the Welsh descend from the Celts as much as the Irish do. The same for Manxmen and women and for the Cornish: all of Celtic descent.
The English also descend to a good extent from the Celts, as many of the original Celtic Britons mixed with the Anglo-Saxons, adopting over time the Anglo-Saxon language and gradually amalgamating into one people.
In fact, in the charters of King Ethelbert of Kent, who lived in the 6th century, there is mention of the Britons who were not Anglo-Saxons (or Jutes) and were living in Kent, as their rights are defined and guaranteed in these charters together with the rights and obligations of the Anglo-Saxons (or Jutes) of Kent.
Similar charters concerning the rights of Britons (Britons = Celts) are found in the charters of Wessex.
These Britons eventually started speaking English, and became part of the English People, in Kent, Wessex and elsewhere in England.
In Northumbria, Brythonic, which is a Celtic language, was still spoken in the 13th century in many villages.
Celtic was still spoken in Cornwall and the Isle of Man in the 18th entury! The Scots were speaking Celtic (both the Brythonic and Gaelic versions) even in the days of Robert the Bruce, but gradually started speaking English.
In the Hebrides, many people speak Gaelic (Celtic) today!
In Canada Gaelic is spoken in some communities of Scottish and Irish descent in Newfoundland.
The people of Edinburgh are originally of Anglo descent (from the Angles), which is why they spoke English there when all the other Scots were speaking Brythonic and Gaelic (both Celtic languages).
Vikings (from Norway and Denmark) settled in northern Scotland, Dublin (Ireland), East Anglia and eastern Yorkshire, but were always a minority, and eventually amalgamated with the local English/Scottish Irish populations.