I think that it really depends on how you define the term "Celt". Narrowly as applied to a fairly local group of people - the Keltoi or as a generic name for Iron Age Europeans - Gauls and Gallitians being names derived from Keltoi? The key thing is that genetic mapping is now showing that 80% of us are descended from the first people to move into Britain after the ice retreated.
Clearly there are common linguistic roots that Britons share with other Europeans. Genetics seems to be indicating that there has been considerable continuity of population since the retreat of the ice with no mass folk migrations. There will have been trade and social intercourse with the mainland and tribal names such as the Parisii of Yorkshire and the Belgae of the south coast indicate some immigration of main land Gauls.
Ditto the famous square barrows of Yorkshire so if there were Celts anywhere in Britain, they were in the east not in the west.
The whole Celtic west phenomenon is what brings me out in a rash and I am reminded of Tolkien' famous line "Anything is possible in the fabulous Celtic twilight, which is not so much a twilight of the Gods as a twilight of the reason". Archaeologists always seem to energetically debunk the theories of the previous generation and the migration theories have been under attack since the 1960s. Simon James and Frances Pryor have really attacked the notion of Celtic migration into Britain and other "archaeologists could be said to be suffering from Celtic denial" as Barry Cunliffe has said in defence of his much attacked position. I am currentlr reading and will shortly publish a review of David Miles' "The Tribes of Britain". I do recommend it as it gives what I consider to be a very balanced view of British population movement and continuity from the "Red Lady of Paviland" to the present.