I was reading up on the legalities of this a while back, and it's basically at your discretion when you think your child is safe, and is old enough.
It's at your discretion but within reason. I came away thinking the law seems to say under tens is too far, but that's was basically a guess because there no minimum age in the law, it's vaigue.
Personally I think it depends on the length of time , and the specific 11 year old in this situation. Some 11 year olds are very competent, have a phone, can use it, would have their bearings in the hotel, be comfortable with the door key.
I would leave my eleven year old in a hotel room of they were comfortable, but only for an hour or two at the most, but not a night out for hours and hours. Plus even when you get back the kid might not be properly cared for if you are pissed.
I bet his mates called it in.