I am a school Safeguarding Lead. If a parent called me and told me another parent smelled of alcohol on the school run, I would listen, record the information and ask the child's Form Tutor to find an opportunity to discreetly check in with the child to see if they raised any worries or concerns about home.
Contrary to what some posters have suggested, I absolutely would give assurances to keep your confidentiality, and stick to them. I would log the concern as "a parent of a Year X child has reported..." rather than giving your name, which would be unecessary. But the other parent and her DC also has a right to confidentiality so I wouldn't be able to tell you anything about what, if any, action I intended to take or whether or not I was already aware of difficulties within the family.
Aside from that, there would not be much I could do. It's not illegal or inherently abusive for a parent to drink to excess. Parents are allowed to make what many of us would consider to be poor life choices, and it's not a schools place to judge or intervene unless there is a demonstrable impact on the childs wellbeing, safety or ability to access education. For it to be a clear safeguarding concern the parent would have to be in sole charge of the DC at the time they were drinking, or unable to care for the child or get them into school the next day due to being too hungover, or there would have to be indications that their drinking was causing the child distress. In OP's case there is no evidence of these factors so we would monitor the situation but there would be little we could do in the way of immediate action unless the child made a direct disclosure or it was part of a pattern of wider concerns.
That said, as a DSL I would always rather a parent who was worried about a child for any reason called me than not. Even if it turns out to be nothing. For all you know, OP, this could just be one small piece of a puzzle that school have been working to put together for some time.