The planning permission for T5 required it to be water neutral. So every drop of you shower suds need to be slurped away and recycled into BA coffee (I presume). Sounds like the coffee machine is on its last legs.
You can minimize the sound by sacrificing the smaller of the two towels you have (or use a flannel if you travel with one). If you put it so that only about 6 holes in the grill are exposed it transforms the noise into a more congenial gurgle. Use your big toe to control this.