They're businesses, they charge what people will pay. While risky, as an investment, an LSE masters works out pretty well. Sure, you have to borrow a lot, but it's a big boost for a CV. And really, that's primarily what a masters is. If you want to go into research, there are a lot of 1+3 scholarships so the tuition need not cost a penny. The only people reason to pay for a masters is if you don't want to do a PhD (which likely means you want a CV boost) or aren't good enough to get funding for one.
The idea of the class system separation is important at undergraduate level, as many jobs require a degree, and thus class mobility requires that people from poor backgrounds are able to get a degree and become better off. At postgrad level there's no need for this, as the only jobs that require a masters are research-related fields that generally you'd do a PhD for, which there are scholarships for. Or are jobs where the employer would usually fund you fully for a masters (like law or economics).
Paid masters are either a CV boost for those who fail to get into what they want, or education as a consumption good - people just wanting to study more. Where it's needed, there's funding for it.