According to most linguistic / historical sources, the English language as we know it today is a West Germanic language (the other two languages in this family being German and Dutch). Modern English is the descendant of Old English, and Old English was essentially born when the Anglo-Saxons migrated to the isle of Great Britain in the 5th c. C.E., from their traditional homeland in the north-west of modern Germany. Prior to this time, it's believed that the inhabitants of all parts of the British Isles were predominantly Celtic speakers, with a small Latin influence resulting from the Roman occupation of Britain.
Of the languages that have influenced the development of English over the years, there are three whose effect can be overwhelmingly observed in modern English: French ("Old Norman"), Latin, and Germanic (i.e. "Old English"). But what about Celtic? It's believed that the majority of England's pre-Anglo-Saxon population spoke Brythonic (i.e. British Celtic). It's also been recently asserted that the majority of England's population today is genetically pre-Anglo-Saxon Briton stock. How, then — if those statements are both true — how can it be that the Celtic languages have left next to no legacy on modern English?