It was mid-morning and the only people in the whole of thentire police station were still Constable Twitten and Mrs Groynes, the station cleanejanitor.

You don’t have to write mid-morning. Just morning will do you just fine. Also, you usually use “entire” instead of “the whole of” since the latter expression is not entirely correct. Lastly, the occupation you have if you clean for a living is called being a “janitor” not a “cleaner”

The two of them picked up their conversation—Mrs. Groynes had previously left the room to go and prepare the tea—prepared some tea for the two of them and they continued their conversation about the last murder case.

Putting the explanation about what Groynes did in the middle of the sentence is rather awkward. It would be better to have it at the beginning. You can say “picked up their conversation” especially after the rewrite “continued their conversation” sounds better, at least in my opinion

Twitten still couldn’t understand who had actually murdered Braithwaite, and voiced as much to Mrs Groynes.

The notion itself that this woman knew more than him was seriously eating away at his confidence; he felt like he had failed at the only thing he was good at, that is, working outsolving mysteries.

Mrs Groynes revealed to him that Joanna Carver was the perpetrator.

It seemed thatlike Braithwaite and Carver had gonewent to school together when they were younger.

One day Braithwaite had intentionally injured Carver during a gym session.

She never got over it afterwards,the incident and as a result she became quite short-tempered.

So, when she bumped into himer a few days ago, Joanna fiercely attacked him.

I think you got your subjects mixed up. Doesn’t it make more sense for he to bump into her and make her angry?