welsh ans gaelic are definately related. the term celti first occurs in spain among the celriberians who called them selves celti, and inscriptions of theirs go back to 1200 b.c., in a script derived from phoenecian and iberian use of phoenician. julius caesar refered to the people between the loire and the pyrennes as celti as well. it's an old well know term.
there is a lot of british empire hangover racism when the english try to prove celts didn't exist. not unlike south africans proved that the blacks of the cape didn't exist.
geneticlly there are identifiable familial lineages unique to the celtic fringe on england and scotland as well as ireland.
the celts were probably one of the two first peoples in the celtic isles. the other a mediteranean farming people in ireland first.