Can an employer legally refuse to allow me to go on sick?

As title...

Provided I supply medical evidence to support my claim of work-related stress, exacerbatiom of depression and stress. Can the employer reasonably refuse or refute my application?

I dont feel comfortable telling my boss or her immediate Management team or Senior Managers. Im going to email how I feel to Human Resources, and document the fact im going to go to doctors. They are aware I suffer from anxiety but not aware ive been on meds for the last 8/9 months. Ive also had a fair few number of absenses due to illness (though didnt state it was for mental healfh, told them it was sickness and diarhoea), and I just dont feel comfortable to tell ghem. The job itself is fine- its the environment, staff and the undermining of peoples abilities.

Ive recently had runnings with managers over timetabling issues and trying to get my shifts covered because i cant get to work (no transport bank hols and no money to pay for taxi), they rejexted the cover i got and are been awkward. Telling me i shouldve arranged well in advance...yet the rota for new years was only released xmas day.

You need to be honest too you know. You can't just claim an ongoing illness as one-off incidences because that looks pretty suspicious

I havent claimed anything to be of a one-off nature. At some of those times I was suffering sickness and such due to stress. My mental health concerns were only made worse by the workplace politics and bullying, harrassing of other colleagues which ive been witness too. My GP recommended I go on sick and suggested it to me last time. But I dismissed it becauss I was woddied about the financial burden.