Council demanding £9,000 for change of use from guest house to HMO

I would be grateful for your advice on the following HMO application matter.

I am in the process of applying for a HMO licence for a 7 bed house which my son shares with his friends. They are all post grads, studying medicine in the local medical school.

The City council has approved the HMO application but require me to sign an Unilateral Undertaking of contributions to the council. This I have been informed is a legal agreement, for contributions required in accordance with the Council Planning Obligations Strategy and Local Plan policies 3/7 and 3/8. I also have to pay for the legal fees for this. 

I have disputed the contribution requested, which comes to over £9000! These included contribution to Informal Open Space, Outdoor and Indoor Sports facilities, Community Facilities etc. I have put forward the argument that the students will have many facilities that are available to them, at the hospital, medical school as well as their undergraduate colleges to which they still belong. These include many social and sports facilities.

However, the response I received was:

As for the contributions, they are correct and payable. The Council cannot take into account the facilities provided either by the colleges or the hospital, because once the use as a HMO is granted, it could be occupied by anyone, and many future tenants will not have access to these facilities.

I really do not object to some contribution to the community, but I think a request for over £9000 is a bit extortionate!

Is this Unilateral Undertaking a legal obligation, as I have not heard or read about this?

Many thanks for your advice.

Kind regards

Alice