Negligent landlord in university student housing- RATS

Hello, I am a university student in England and in student housing.

I began my tenancy 1st July, there is a mountain of rubbish and old soggy cardboard boxes filled with more rubbish left be the previous tenants in the garden.

We have been asking our landlord to move that rubbish for 7 months and he hasn’t and we are starting to get rats in our garden.

I planned on reporting him to the letting agency but their ‘complaints email’ is hisname@lettingagency.com so i’m inclined to believe he owns or has a high level of control in the company. So I gave up on that idea.

Any advice?