What are polite appellations for teachers in British universities?
Here's an answer based on my experience in the United States.  I don't know how well it generalizes to other countries, but some issues may be similar.

You can't go wrong calling someone Professor or Doctor unless you know for sure that it is inappropriate and they know that you know.

At the college level in the U.S., it's common to refer to your teacher as Professor X regardless of whether their official job title includes the word professor.  (The primary teacher of a college course is considered to be acting as a professor for that purpose, even if their official title is visiting scholar or postdoctoral associate or whatever.)  This may not apply to grad students, but it can cover just about everyone else.

When possible I'd avoid gendered titles like Mr. or Ms., and specifically Ms.  The issue is subconscious sexism: some people tend to use fancier titles to address men than to address women in comparable positions, and calling someone Ms. may make her wonder whether you are one of those people.  (If you are such a person, then you should mend your ways, and even if you're not you could still be mistaken for one.)

On the other hand, Miss and Mrs. are far worse than Ms., because they indicate marital status.  You should never address an academic as Miss or Mrs. unless she has explicitly indicated that this is what she prefers.