Rent control, and price controls more generally, are stupid. It doesn't solve the problem of demand being far higher than supply, which is why it never really works.

I just get sad every time I see it.

In the UK, there is Council Housing, this may be a good alternative to rent control because it provides housing at a nominal cost and gives the private landlords some competition. The only problem with this type of offering is it will stick in the craw of the American psyche who abhor the government competing against the private sector.

Rents do get bid up due to things like the minimum wage rising. This is because the power relationship between landlord and tenant is heavily skewed in favour of the landlord. The employee/employer relationship also suffers from the same disease.

Disclosure: I'm a US/UK dual citizen, and a landlord myself.

"because it provides housing at a nominal cost and gives the private landlords some competition."

Sincere question as I don't know much about the UK rental market: why aren't the private landlords in this segment of the market competing with each other? Is it difficult to build additional rental housing cheaply enough?