I live in the UK and I look at a country like Germany that has much stricter rental laws than the UK (including rent control policies) and I see a superior system. It seems that tenants in Germany enjoy much better security of tenure as well as protection against rapid or unfair rent rises. So it seems that rent controls can work.
What's partly happening in London is that the housing market is overun by buy-to-let landlords and "property investors". They are often chasing the same properties as first-time buyers, adding to the rise in house prices. If buy-to-let activity was curtailed (for example by removing certain tax advantages), it might dampen some of the pressure on house prices. (However, it's highly unlikely to be regulated more tightly given that many of our MPs have second or third properties).
Strong rental laws (including rent control) might actually help deter the worst type of property investor or buy-to-let owner: put off by the responsibility to comply with such laws. It doesn't mean that someone can't make money from property if that's want they want to pursue. But rent control laws send out an important message to wider society: that housing can't be treated as just a pure profit-making exercise. It has a social component that simply cannot be ignored.