Law or otherwise, I don't see how this would have a big impact on rents. The landlords can't declare themselves immune to supply and demand - there is a market price and if their rents are too high the housing will be empty. They can't form a big monopoly by talking to each other, because the cost of having empty properties will fall on specific landlords who then have incentive to defect and go towards the market price.

I'm sure the scheme is helpful to landlords at some level, but it'd be a bit weird if it was more than a marginal difference in rents.