I'm not familiar with the housing situation in Britain, but in the US housing is absolutely a capitalism problem. Affordable housing development has been neglected for decades in the US because there is less profit to be made compared to luxury housing. This is just one way housing has been transformed from a basic necessity into a speculative asset, it has gotten so bad that most Americans who do not currently own a home will never own a home.
As soon as houses are put up for sale corporate Real Estate Investment Trusts (REITs) are bidding like $50,000+ over asking price, much more than any ordinary family or individual can afford. The result is a massive housing shift, previous generations of Americans owned their homes, the younger generations will rent their homes from a merciless corporate landlord forever.
The benefits of a mixed economy including subsidized housing used to be non-controversial, but over the last 50 years conservatism shifted the Overton window far enough right that even suggesting moderate government regulation is a non-starter. It is no surprise to me that young people are galvanized to push past more moderate solutions unwaveringly leftward. The systems that are in place are failing the youth and will regressively continue to fail every generation that follows.
Change needs to happen, I have seen it at every level of our society. The public is crying for peaceful change, but as changes are slowly implemented it feels too little too late. It is no surprise to me that people want change and they want it now. The rise in radical polarization is the public crying for change and the body as a whole unsure what direction it wants to go. The way to resolve these situations peacefully is to have these hard conversations out in the open, to encourage discussion and widespread participation.