Cancellation - I have to pay

I signed up with Chubb after they said to me I get a free alarm system installed and I do not have to pay for it. I recently got offered and better deal with another company so want to cancel and have now been told if I cancel I need to pay a penalty fee and they will remove the system as it does not belong to me yet. When I initially signed up i was told that I could cancel on the day they installed and only need to pay for three months as a penalty fee or if I paid for 3 months and then cancelled I would not be charged anything extra and the alarm system is mine to keep. They will only remove the radio as this belongs to Chubb. I initially queried this two weeks ago and only after i followed up today I get told the same thing. and the penalty fee. I would like an explanation how I have been sold something under false pretences and when I want to cancel I get told about additional extras at that stage. I am awaiting feedback from the response I got and gave and will then take the matter further