The only official languages of the United Kingdom are English and (in Wales) Welsh. Great Britain as an island does not have official languages. There are other spoken languages like Gaelic and Manx (on the Isle of Man)
Technically, Great Britain doesn't include Northern Ireland as it refers to the island. Though "Britain" is used to refer to full country is the United Kingdom of Great Britain and Northern Island and (I think) the Channel Islands. So no Irish Gaelic I don't think.