Hannah had come into conflict

[Bassim]

I feel that my sentence does not sound natural. Would you please correct my mistakes?

Hannah had come into conflict with her boss, who demanded she wore a dress with a deep cleavage and high heels, or quit.

[teechar]

I don't know where you get these contexts from!
Lose the second comma, and switch "a dress with deep cleavage" and "high heels" around.

[Bassim]

teechar,
There were a few cases in the UK reported in the media where women were ordered by their bosses to wear high heels and deep cleavage or quit. Last week there was a discussion about it on a talk radio station where many women called in and told their stories: waitresses, shop assistants, receptionists, secretaries etc.

[GoesStation]

We'd use the subjunctive mood in AmE: ...her boss, who demanded she wear​....

[Bassim]

I wanted to use the subjunctive mood in my sentence, but I was not sure if that would be correct in BrE. I am wondering if the subjunctive mood would also be correct in BrE.

[teechar]

teechar,
There were a few cases in the UK reported in the media where women were ordered by their bosses to wear high heels and deep cleavage or quit. Last week there was a discussion about it on a talk radio station where many women called in and told their stories: waitresses, shop assistants, receptionists, secretaries etc.

That's absolutely appalling!
Mind you, given that the media format mentioned is talk radio, I wouldn't be surprised if they're blowing it out of proportion to sensationalize the issue and gain more audience, as is their wont.

[Bassim]

teechar,
It is the well-known talk radio. I do not need to name it, but you probably know which is the largest talk radio station in the UK. It is a commercial radio, but I listen to it because I can hear ordinary people talking, like bus and taxi drivers, the unemployed, pensioners, but also well-educated people. They are calling from all parts of the UK, and you have an opportunity to hear all kinds of stories. Of course, you cannot always prove what they are saying is the truth, but for me it is a an important source, which give me an opportunity to hear spoken English.

[Tarheel]

Some men will do whatever they can get away with.

[Rover_KE]

I wanted to use the subjunctive mood in my sentence, but I was not sure if that would be correct in BrE. I am wondering if the subjunctive mood would also be correct in BrE.

It would be correct, but the subjunctive does not come naturally to a great majority of BE speakers.

[Phaedrus]

It would be correct, but the subjunctive does not come naturally to a great majority of BE speakers.

How about the modal variant with "should" ("who demanded that she should wear . . .")?