Broken heating in halls

My heating broke in my student halls on a Monday. I reported it online and the online system said that someone would be out within 24 hours as it was an urgent repair. I had not heard from anyone until the following Monday when I decided to ring up about it at approx 10am. I was told that they had to get an update from an engineer and that I would receive a call back. I had not heard by 3pm and rang again only to be told that I would get a call back by the end of the day. I did not receive a call. I rang back on Tuesday and they said they were still fixing it. I found out the person staying in the room below me also had no heating and they had submitted over 5 requests and had not heard anything either. I was told that someone did call on the Tuesday after reporting, but they didn't leave a call-card or update the online system. I was not offered an electric heater or alternative form of heating. I was sleeping in a cold room every night where the corridor which had open windows was warmer than my room where the windows were closed. It got so bad that I went home for the week to get some heating. I have medical conditions (which they are aware of) that makes me more sensitive to the cold. I pay a large amount of rent per week for accommodation which is supposed to include heating. Given that it was broken for 2 weeks, I would like to be recompensed for the rent and for the lack of updates as to the progress of my repair request. As far as I was concerned, I was just being brushed under the carpet. My halls are refusing to refund any money, but I was wondering where I stand on this matter as they have not obligated their part of the accommodation contract to provide heating at the said times and failed to respond to my request in the set time frame.

Thanks in advance.

TL;DR - Can I be refunded rent for broken heating and not being notified of update on repair request?