Thanks for posting the link to the Regulations, OP. It's interesting to see how they differ from the advice we've been getting.
I do think the simplicity of the advice is a virtue, even if it goes further than the law. People need a short simple message that they can remember. Also, just because something is permitted under the Regulations it doesn't mean that we should do it. We shouldn't leave home for multiple shopping trips just because we can (those like the poster who is doing shopping for different households are exceptions).
We can go out for basic necessities. Food and medical supplies are given as an an example, along with supplies for the basic upkeep, maintenance and functioning of the household. That's a pretty wide category I'd say.
Until I had to self isolate last week, I had been buying food and collecting prescriptions for neighbours. One elderly lady asked me to buy her a newspaper every day. I refused, saying that I would get one if also going out for food, but wouldn't go just to buy a paper. I guess one could argue that it was a basic necessity, and even if it isn't I could get round the restriction by buying a bar of chocolate at the same time so that I could argue I went out for food, but I felt that a special trip went against the (in my view sensible) advice to go out as infrequently as possible.
Most people will be sensible. I do worry a bit about the police overstepping the mark. But, at least at the moment, I worry more about the idiots who completely flout the law or those who will deliberately push it to its limits by insisting on exercising their right to do something that isn't necessary but hasn't been prohibited. If think the inevitable consequence of that would be a tightening of the restrictions. If we need that because there is a scientific need, fair enough, but if it will be annoying if it happens only because of the behaviour of a small minority of people.