Rent control will lead to more slums and more boats like this. American cities have tried rent control, and it simply leads to a shortage of rooms for rent. After all - why would you build apartments or rent out existing rooms if you're not going to make money off of it?

If you're looking for a leftist answer that would alleviate some of this, I would suggest running with the platform of subsidized rent. In the US, it's called Section 8, after the section of the 1937 Housing Act that created it. Basically, if you earn less than a certain amount of money, the government will pay for a certain amount of your rent (ranging from a small portion to almost all of it). In turn, landlords are guaranteed tenants and funding as long as they adhere to certain building requirements and responsibilities.

Section 8 ends up getting a whole bunch of criticism, as it drives housing prices up further and dicks over the middle class, (if you don't qualify for assistance, you're going to have problems) but if you want to make it a priority to have working-class / poor people live in London, that's probably the way to go. You have to pay for it with increased taxes, though.