Difficult to say unless you were there if this was a jobsworth or not.
I had a summer job in an off licence whilst at university. I only once refused someone on the grounds they were buying it for someone else - in this case her (adult) sister who'd I'd refused a few minutes prior because she was absolutely paralytically drunk.
Ended up with both sisters in the shop ranting at me and refusing to leave, accusing me of being racist. My colleague just quietly called the local police station who turned up and told them in no uncertain terms that it was private property and if the were asked to leave they must leave, end of. He gave them one more chance before the cuffs came out and after that they disappeared pronto.
Best part was they both then barged in the next morning complaining to the manager and wanting me sacked. Helen was a fearless Scot who told them if she ever heard of them abusing any of her staff again they'd be barred for life. Off they went with tail between legs, both nice as pie after that incident!
Having said all that, I don't think I'd ever refuse a parent even if I did think they were buying for their child. I don't think it's actually illegal for a parent to give a child alcohol anyway.
AFAIK, the law doesn't specify a test of reasonableness.
Indeed. You can be refused service just because the shopkeeper doesn't like the look of you, and there's nowt you can do about it. So long as they don't say it's because of your race, religion or other protected characteristic you just have to suck it up.