I work in the complaints team for a major retailer and regularly get complaints about this type of thing. The two main aspects to think about with age restricted products are underage sales and proxy sales.
If you look under 25 (and it is about the perception of the person serving you not your own perception) they will ask for ID and if you don't have it they won't sell it - this is the law, the only person who can change this decision is the responsible person. This is either the licence holder or the person acting on behalf of the licence holder (normally a manager or a supervisor). It's very rare for them to go against the original decision. The reason for this is they do not want a staff member to be to afraid to question in the future and potentially let an underage sale go through.
If a staff member has already refused and sale and then let someone else buy the product for that person, they are allowing a proxy sale - this is also against the law and can incur a personal fine of 5k, loss of license for the business and additional business fines too. This is why they may ID everyone with you, and why you cannot buy on someone else's behalf.
When it comes to children being with you, it is not necessarily the case that you will always be refused. It depends on lots of different factors, it would be rare for you to be declined with say an 8 year old. That being said, if you child has carried the alcohol, pointed it out, or paid any real attention to it you may be refused. The reason for this is that the whole system relies on perception (it is this way by law).
If you are going in with a 15 year old and you are buying alco pops there is a very high chance that you will be refused. As many parents buy alcohol for children of that sort of age and that tends to be the type of alcohol teenagers favour.
To be honest it is more about who may be behind you in the queue.
If it is someone mystery shopping from the council and they see you being served when they think there was something suspicious about the sale (you could have potentially looked under 25 or be buying for someone else) the store will be fined as well as the cashier even if it could be proven you were old enough. So you may even be ID'd by someone you know.
Also the next person could genuinely be to young to buy, and if they are ID'd when you are not and you don't look too dissimilar in age, this could cause conflict and put the staff member in an awkward situation.
In short, if you think that you or someone with you looks under 25 takes ID and if you do have children with you, don't like them 'interact' with the age related product. If they are a little older (I'd say 13+) avoid taking them with you or having them at the till.
At the end of the day would you want to pay a £5000 fine just so someone could have a bottle of wine? Or lose your job to stop a slight inconvenience?
Probably not.