Blushingsnail's post indicates that the planning permission specifies no noise should be heard outside the gym at any time:

"No music, amplified sound system or other form of loud noise (such as singing or chanting) shall be used or generated which is audible outside the premises or within adjoining buildings."

I don't see there's any question of the gym having to close, but according to the terms of their planning permission they are required to either turn the volume down so that the noise can't be heard in the flat above, or get appropriate soundproofing.

It would be interesting to hear Energie's side of this. Are they perhaps not convinced that the noise can be heard upstairs? Have they been up to listen yet?