It all depends on the terms of the contract which you entered into.
Generally the only contracts with a cooling off period are those done over the phone and sometimes the Internet.
If the contract states 3 months rent on termination then that is what you are contractually obligated to pay. What you feel is sufficient is not taken into account. This should have been agreed upon before the contract was entered into and reflected as a term in the contract itself.
I appreciate that you may not like this answer as it conflicts with your statement above as to what you feel is sufficient in the circumstances but it is the legal position. I have confirmed the legal position at least.
If you wish, as an additional service, i can review the termination provisions and advise if there is anything which you can do legally.
Do you have any queries or questions in respect of my answer? I am happy to assist further.
Please can I ask you to accept /positive rate my reply otherwise the website will not pay me for assisting you. Many thanks.