Indeed.
At which stage you write a clear and concise recorded delivery letter to the head office. I personally would further supplement this with video and photo evidence of just how busy the gym is at the time that I was trying and unable to use it. Not only would this strength a case that you aren't getting the service you paid for and wish to terminate the contract, as a result, it may make the gym reconsider numbers and possibly introduce a minimum time per machine during busy periods, making it better for all users.
Has has been said though for the billionth time.... The OP did not do that, he cancelled his direct debit and has no recourse because there is nothing lodged to show his dispute with the service.
Live and learn.