Do you think it would be illegal

for a gym to monitor machine usage over a period of time without telling gym users? 

Faod i think the answer is no if they don't have names attached but it's bad form not to tell them.

Sorry I explained badly.

During a certain period it monitors people using the machines (all machines). So they know who is in the gym and which machines are used and for how long but not who is using each.

So they know that 

1. Treadmill 3 was used for 36 minutes from 7:30pm to 8:30pm.

2. That Clergs was in the gym from 7:30pm to 8:30pm

But they don’t know whether you used treadmill 3, or just spent the time perving at all the pretty young things in lycra?