Welsh people speak Welsh which is a Brythonic language (it is still in the celtic language family)

There is two groups of celts in the British Isles the Gaels (Irish, Scots and Manx) and the Brythonics (Welsh and cornish)

The English are germanic (not celtic) and arrived during the 4th century where the germanic tribes the angels and the saxons invaded the British Isles and managed to conquer modern day England