English is the descendant of Old English, or "Anglo-Saxon", which was really a set of dialects spoken by several (West) Germanic tribes including the Angles and Saxons:
https://en.wikipedia.org/wiki/Anglo-SaxonsGermanic is one of the branches of the Indo-European languages, including Slavic, Romance, Indic, etc.
https://en.wikipedia.org/wiki/Indo-European_languagesAnother branch is Celtic, which at one time was spoken in the Iberian peninsula (Spain and Portugal), mainland Europe (a common enemy of the Romans) and also the British isles. But like Germanic it originally arrived by invasion of Indo-European peoples; it wasn't a native language either.
https://en.wikipedia.org/wiki/Celtic_languagesThe Celtic languages survive today as minority languages in the British isles (Irish Gaelic, Scottish Gaelic, and Welsh; Cornish and Manx are extinct although there are some revitalization and education efforts). And Breton is now spoken in northern France, after being displaced from England.
https://en.wikipedia.org/wiki/Breton_languageThose are all the "Insular Celtic" languages (as opposed to mainland Celtic, of which none survive today and for which there are only minimal historical records and texts). They can be divided into the Brittonic branch including Welsh, Cornish and Breton:
https://en.wikipedia.org/wiki/Brittonic_languagesAnd the Goidelic branch including (Scottish and Irish) Gaelic and Manx:
https://en.wikipedia.org/wiki/Goidelic_languagesBefore being displaced by the Germanic invasion, all of these languages were more widespread, so part of your answer is that Welsh, Cornish and Gaelic were spoken in the region you're interested in. But probably the best answer is Breton.
However, there is also a language that is of uncertain classification, Pictish:
https://en.wikipedia.org/wiki/Pictish_languageThat's the oldest known language from the British isles. Although it too might not be indigenous if you were to find out enough about the history of migrations, its history is not known so it's the only language without a known history of migration into the British isles.
Looking back even further, some linguists have suggested a substrate (a socially non-dominant, non-prestigious language with an effect on the dominant languages "from below") of Afro-Asiatic origin (that is, related to Arabic, Ancient Egyptian, etc.), although this is controversial.
There of course have also been invasions and linguistic effects from the Romans, Norse and Norman French, but they didn't leave any permanent languages behind, nor did they replace any languages spoken there. (The only exception would be Norn, a north Germanic dialect related to Faroese and Icelandic, once spoken in some of the northern Scottish islands, but it died out several hundred years ago, replaced by Scots and Scottish English.)
