No.
1. This isn't a widespread thing. No idea how you've decided that it is.
2. How does overfilling properties lead to rising prices? If anything, it would serve to keep prices lower.
3. Which authorities are "in on the shuffle taking kickbacks"?
When one family rents a 2 bedroom flat, they may be able to afford say 1K (husband and wife working). But when the same flat is rented to 4 singles, they might be able to afford 2000. Each person's share is just 500. So when the landlord asks them 1200, they would happily pay for it as the effective rent per person is only 300.
A friend of mine lives somewhere in North London (I believe it is Golders Green), paying 1300pounds a month for 2 and half room apartment, paying council tax and so on, all on a minimum wage as a porter which is around 1200 pounds a month(why he prefers being a porter over a Perl programmer that is one of his skills is another question).
If he were not subletting the room and half, there would be no way he would be able to work in London for a minimum wage. The situation is similar to most people working for minimum wage that he knows.
Still, I think this overfilling is a symptom not the cause of high property prices. This overfilling by the poor has always happened in big cities.