Many thanks for your question.
Without having all the details and documents this is my assumption on the facts provided. You are quite right that lessor is landlord. Lessee is a tenant. The company to whom you pay the ground rent is a tenant of the freeholder under a head lease. You therefore have a sub lease and are a sub tenant.
You can check this at the land registry. It costs a few pounds to get a copy of the title. If you sign up to the land registry you can do a map search. You pop in your address and you will see an OS map of the locality. Click to see title numbers, click on your property then you will see the registered titles. You can then find your landlord's title and the freeholder' title. You can download the title as a pdf, you can also download a copy of the leases, if you wish. The title will show the owner's name and address.
Also check your lease to see if there is a clause in it whereby you can request the landlord enforce a covenant on another tenant. A well drafted lease should include such a clause. You can then make a formal request for the landlord to enforce the covenant (you might have to pay the landlord's costs/expenses).
I hope my explanation and response is helpful. Do please let me know if you have any queries in respect of my response. I am happy to assist further.
Please can I ask you to take a moment to accept / positive rate my response.
I will look into this during the morning and respond.