Thanks for your email. The further details provided make the position much clearer.
I think we can therefore disregard all of what was said about you being notified about the change in landlord. As a managing agent is involved this is the person, on behalf of the landlord, who would be responsible for ensuring that issues regarding the property are dealt with.
I understand the main issue here us that you want to be compensated for the inconvenience suffered.
Whilst I fully appreciate that you would have gone through an unpleasant and distressing time whilst the boiler was broken we have to consider if you have suffered loss. This will be difficult to establish.
You need to establish (1) financial loss (2) pain and suffering.
Re (1), you have told me that you did not pay for the repairs and therefore suffered no direct loss. However, we can consider indirect losses, for example did you buy an electric heater to keep the property warm, boiling more water in the kettle in order to wash etc and increased electricity bills, travel costs to shower? If not, then there is no associated financial loss.
Re (2), pain and suffering. Whilst you may have been cold during this period and caught a cold you have to be able to quantify this. This would be nominal.
If you did incur indirect losses as described in (1) above then you could potentially bring a claim. In addition, you would have to establish that your landlord was in breach of his duty owed to you. Your landlord may be able to demonstrate that he did what he reasonably could to ensure the boiler was repaired asap. It did happen around Christmas and new year which is a busy time of year. You do need to consider your chances of success and balance this with what you are claiming and the associated costs of bringing a claim (you have to pay court fees based on the value of your claim). Therefore, you could end up out of pocket. I cannot advise on your chances of success.
Also consider that if you were to bring a claim against your landlord it may result in the landlord serving notice.
What are your losses exactly?