Hello, I am a solicitor with 20 years experience. I will try to help you with this.
Firstly, your landlord can not use the police to get you removed. He will need to serve a notice seeking possession the go to court to get a possession order before he can do that.
Even then he can not use the police to evict you.
None of your agreements with the landlord are in writing I think. So your status will be that you are an assured shorthold tenant and the landlord would probably be able to get a possession order relatively easily as you will be on a rolling monthly or bi-monthly tenancy and he will have a right to possession if he follows the correct procedure.
The landlord does have a duty to keep in working order the facilities for heating in the flat and he is clearly in breach of that obligation. However, bearing in mind you weak security of tenure, this ill be hard right to enforce.
Have yo aid a deposit at the flat.
You have no right to withold rent from the landlord and I would suggest you do not do so.
I don't know what outcome you want here. If you let me know what you want to happen I may be able to give you more useful answers.