There's a growing number of calls for rent controls here in the UK. This really isn't all that sensible an idea for as has been pointed out before [3]:

Swedish economist and socialist Assar Lindbeck commented years ago that, “In many cases rent control appears to be the most efficient technique presently known to destroy a city—except for bombing.”

As Mark Perry goes on to point out this has implications for that most recent disaster in Mumbai, when an apartment block collapsed in the night, killing scores [4]:

Mumbai’s buildings department is known for its corruption, and bribing inspectors and other government officials is considered part of the normal cost of doing business. One result is that many buildings are visibly crumbling. Another problem is rent-control rules that allow tenants to live in apartments for a few dollars a month and even pass those rights on to their descendants, giving landlords little incentive to invest in building maintenance. The city requires extensive approvals for even minor repairs, a process so cumbersome that repairs are often either delayed or done illegally and without consultation from engineers.

Rent controls are exactly like any other form of price control. If you set the price above the market price, as we've been doing with farming for decades, then we'll get a glut. If we set the price below that market price (as has always been true of rent controls, always, everywhere) then we'll get a shortage. And that shortage will come about in two ways. Less new building than otherwise will take place and extant building will not be maintained leading to appalling tragedies like this one.

There is of course the vague possibility that the government might stumble across a rent price which doesn't cause either shortage and decay, nor a surplus, but at that point said rent controlled price would be exactly the same as the market price so why bother?

The real question we should be asking those who advocate rent control is, well, so why is it that you want to reduce the quantity and quality of housing in the UK?