Surprisingly, there is no law declaring English the official language of the UK.
In fact, English is just the de facto official language of the UK, which means it is not legally sanctioned as official but spoken by the majority.
England and Scotland do not have any official languages. Northern Ireland’s official languages are English and Irish.
It’s likely only recognized in Northern Ireland and Wales because they’d already supresed Gaelic out of the Scots. England itself doesn’t need English listed as a language because the ruling class never tried to stamp another language/culture out of Englad they way have Scotland, Ireland, or Wales.
Well for starters you’re missing Cornish off your list.