I let some specialist as Cmacq correct me if I'm wrong.

But...

There's a wide misuse of the name Celt here.

The Celt referred to the inhabitants of Gaul that were first in contact with the greeks in Massilia and Caesar defined them as a sub tribe of gauls living between the Seine and the Garonne. North of the Seine lived the Belgians and south of the Garonne lived the Aquitanians (either a celtiberian or a protobasque tribe).

The greeks made a distinction between Keltoi and Galatoi (the first one living in France, the second referring to the migrating La Tene culture tribes).

The "celts" never called themselves Celts. Gael, Gaul, Goidil, Briton, Cymri (cymbri?), or their tribe name.

As for the "celtic" peoples of the British Isles... The Irish, Manx, Scottish, Welsh peoples are a good mix of ancient Gael, Viking, Norman, English, Pictish and britonnic stock. The lowlanders of Scotland are descendant of Britons and Saxons who joined the kingdom of Alba to form the kingdom of Scotland.

I know people descending directly/undirectly from La Tene cultures call themselves Celts by convention, but it would be like Jewish/Palestinians/Libanese people calling themselves canaanites... Hum...

Anyway, I have O'Neil blood in my veins, but I won't call myself a Celt because of that. That would make me part Gael, though. My paternal ancestor came from a little uphill village in Burgundy. There's a fat chance that his far away ancestors were celts.