Chances at Uni Bath BSc Arch (Hons) or Uni Sheffield's Arch BA Programmes?

Look at the selection criteria (most of them will have it near the entry requirements). Look for a teacher who can speak to the criteria.

Also, UCAS has a section on how to write a reference. When you ask the teacher give them that (kindest would be to print it off, but at least the link), and (same as for US schools) a cheat sheet of why you are applying for this, what makes you a good fit for the course and specific examples / reminders of relevant things from their experience of you. As with your PS it’s not about what a great person you are but how good a fit for the course.