From as early as 1720 the Old Bailey Archives show evidence of Muslims in Britain

1720 “Be Ye all of one Mind. I observed that were a Mahometan”

1765
Witness: “I am a Mahometan.”
Judge: “In what manner are people of your profession sworn?”
Witness: “I touch the book, the Alcoran, with one hand, and put the other hand to my forehead; then I look upon it I am bound to speak the truth.”
(He is sworn upon the Alcoran).