Isn't being shown how to access and read NOTAM's part of PPL training ? If it isn't then it certainly should be.
I don't think any use of the internet is on the PPL syllabus, though clearly it should be given that notams are accessible (practically) only via the internet, and so is weather info. But if the CAA made it thus, they would have to mandate its universal provision on the training scene, which they have no power to do. It's a bit like the idea of mandating GPS for the PPL syllabus - they would then have to mandate its installation in the training fleet, which they could do but they would have a war on their hands from the flight training industry.
My guess is that most schools do have internet access and most of them will allow a curious student to look stuff up, but that applies to people being currently trained. The vast majority of the ~ 20,000 numbered UK pilot population gets nowhere near this.
And it's pretty evident that the 2-yearly check flights do not test this.