There are actually around a dozen indigenous languages in the UK. As well as English there are:

Lowland Scots, a Germanic tongue spoken in the Lowlands of Scotland and (Protestant) parts of Ulster.

Welsh (Cymric) a Brythonic Celtic language still spoken in much of Wales and especially favoured by Syrian refugees!

Scots Gaelic, which is a Goidelic Celtic one, spoken in the Highlands and Islands.

Irish Gaelic (Gallic) is also Goidelic, spoken in Catholic Northern Ireland (the official first langugage of the RoI)

Cornish as discussed, Brythonic.

Manx another Goidelic language, spoken in the Isle of Man.

Apart from those. there are Angloromani used by Roma Travellers, and Shelta, among Irish Travellers. There are three variants of Norman French still used in the Channel Islands: Dgèrnésiais (Guernsey), Jèrriais (Jersey) and Sercquiais (Sark).

Add to that Hindi, Punjabi, Urdu, Bengali, Farsi, Polish, Greek, Romanian, American and Jamaican Creole, and there's a lot of languages here!

And that's before you add Anglish, Esperanto, Latin, Elvish (both Quenya and Sindarin) and Klingon!