Over the legal alcohol/driving limit. And before you get your knickers in a twist I know he wasn't driving but once over the 'safe' limit for driving you're deemed unfit for work, operating machinery etc and I'm pretty sure the police would declare unsafe in charge of a child
No, they wouldn't, not having had two units! Many many parents have two or three glasses of wine on a Sat night and would be right over the drink drive limit which is set quite low, but are still parenting just fine (as long as not driving).
I think being drunk in charge of a child is an old law, applies to public places but not to homes- anyway, you'd have to get the police out to get them arrested anyway.
Nothing is stopping you reporting the parent to social services if you are genuinely concerned with ongoing neglect once the door has shut.
If the person was unable to stand/walk properly/slurred speech, that's a bit different than smelling of alcohol/having bloodshot eyes. The latter indicates an ongoing drink problem, but it doesn't really tell you just how drunk they were at that time point.
It sounds like his drink problem is not solved, and the best thing now is to have a chat with the mum in the next day or two, she may have already alerted school/social services herself to try and get access reduced (and failed), you don't know.