i dont know specifically about LLMs, but my boyfriend just phoned a few unis to ask if he could do an MSc without having done a BSc... they made him talk to admissions tutors, and nearly all accepted him after hearig about his working background.
So i suggest phoning unis youre interested in and asking as they may just make an exception. With a BA, you've got more chance at it than my boyfriend had, and he was accepted by Hull, Warwick, Manchester and Northumbria for an MSc in computer science without any degree, purely on the basis of his background.
You can but try.