Not to dodge your question, but I would really urge your DS to find unis and courses he likes first and pick from the best accommodation options from there.
Some popular southern cities might have higher student prices, but other than that I'd say there isn't too much difference in cost and availability if you're looking in the right areas. Most unis will have a Facebook group or something similar to advertise student rentals - I'd advise going through a reputable letting agent if possible but social media is always a good place to start to see what's out there.
The greatest factor in housing costs is likely to be bedroom size/distance from campus and amenities. Even if your DS chooses a uni where housing is comparatively higher, it should be up to him (within reason) as to whether he chooses a smaller house 30 mins away from his dream uni, or a modern one near campus in a uni that he cares less about, for example. Most students are happy to live somewhere a bit dingy as long as it's safe, but just be aware you might drive the cost up with heating etc if you try and be too careful with money.
Just as a rough indicator I paid £350 per month for a 6-person house right by my campus, in a pretty average southern uni city. This was 5 years ago and the house itself was okay - YMMV though definitely. For a decent, more modern place in a popular city you could be looking anywhere from £400 to £600pcm.
I understand this doesn't answer your question but as a semi-recent uni student you really cannot predict what's going to happen. I know some big cities (Birmingham, Manchester etc) do have rental crises but if you look on student pages there are still rooms being let out. I would say that, anywhere you go, getting in early for the upcoming year (sometimes as early as Jan for a July start) is your best bet.
If you're after specific answers though I'd stick to the midlands/north.