Solution to open grey water waste in the basement?

We are renting an apartment on the first and second floor of a building. No-one else lives here. There is a basement that we do not rent but we are told that we are free to use it. It seems that years ago a shed was built in the garden and over the wall of light, where lies a well for grey water waste. This is now in a small room in the basement and the well is open and has never sealed. Of course this is now causing a moisture problem in the whole basement (around 75% RH without a dehumidifier). There are no windows, but a just a few air escapes into a ventilated basement next door and into the groundfloor corridor/lobby. A small dehumidifier and some ventilation brings humidity down to 70%. While the landlord won't do anything about it, for the time being, I am trying to find a temporary solution. I thought of sealing a simple styrofoam cage around the well and the pipes, to contain the humidity produced and the smell. I can provide more details and photos. I am looking for advice. Thank you! Miles