Hello, thank you for the question.
I am a UK qualified solicitor and happy to help.
I presume you have not notified the environmental health department at your local council of all these housing issues?. If not I would ring Manchester City Council as soon as possible and ask them to inspect the property. They can carry out emergency works and can bill the landlord (and fine them too).
By law, landlords must provide heating and hot running water to the property. If they do not, they face prosecution by the local council and can be fined. If for some reason the council cannot help, you would either have the option of paying it yourself and withholding rent (not applicable here as you have already paid), or to instruct a heating engineer to come out and fix the problem and you then pursue the landlord for the money.
If the landlord does not pay or if they refuse for whatever reason, you can sue them in the county court for your losses on the money claim site (www.moneyclaim.gov.uk) although I recommend sending the landlord a letter before action to warn them of your intentions first and allow them 14 days to reimburse you. If they do not reimburse, you are free to issue a claim.
I hope this helps - if you can please accept the answer and give me a 5 star rating, I can answer follow up Q&A's at no extra charge and Just Answer will credit me for helping you today.