Just an update on this situation.
The teacher demands absolute silence while I'm teaching and kids must put up their hands when they want to speak.
At first I thought I'd never get them to enjoy English, but actually they're used to this discipline, and they don't need warming up. So it's working very well.
We do play a few games but never ones that involve more than one or two standing at the same time.
So, it is possible to teach children without resorting to games ALL the time!