History with war studies at KCL is his top choice. Not many unis offer it though - although DH has discovered Wolverhampton do and is raving about cheap accommodation there
No, no no, to Wolverhampton! Frankly, please insist that this is a false economy. THey've just closed down and entire school in the arts & humanities, they are not research-led, and while History graduates are very employable, a degree from Wolverhampton in History is, sadly, not an attractive offer to employers. Your DS will not be pushed or stretched, because the overall standard is so much lower at post-92 universities.
If you're going to do a generalist Humanities degree go for the best research-led university your A Levels can get you into. Anything less is a waste of money.
If your DS is aiming at KCL, Exeter & Bristol, he might look at Birmingham for War Studies in History, or York or Lancaster. All those departments are well-regarded and in the ballpark of his first choices. And Birmingham housing is plentiful in Selly Oak (don't know so well about halls). York & Lancaster both "cheaper" northern universities, with excellent Arts & Humanities provision (and sport - the Roses each year being one highlight!) Their History Departments are very good, as is the History Department at Leeds.
The difficulty/cost of housing in London, Exeter & Bristol is partly because none of these cities were big industrial 19th century cities with mass workers' housing.
Frankly, your DH is being ridiculous, and your DS needs to get a proper summer paying job.