@maximadewit
No need to pile on the poster. It's a perfectly reasonable question.
No it's not!
No wonder people are 'piling in' on the OP. What kind of question is THAT? Why the hell wouldn't someone pay rent on a council house? Come ON. Surely no-one is clueless/daft enough to think that people don't pay rent in social housing? I call bullshit! 
And it's quite an insulting 'question' actually. 'Oh I need to ask a question; do all you council house plebs people get your accommodation for free?' head tilt...
Same kind of twatty way of thinking as the people who think social housing/housing association properties are subsidized by the taxpayer. 
They are not. And it's almost always people who pay very little tax who bitch about it. Jealousy, that's what it is. Jealousy and ignorance.
We used to have a LOAD more social housing properties before they were sold off by the Tories. There needs to be many more built, especially with the rocketing costs of buying a house. The fact there are 2 million families on the waiting lists in the UK proves there needs to be more good quality, social housing built (with affordable rents.) And tenancies for life.
Some people have said 'if the people on low income are earning 2-3 times more income 7-10 years after moving in, they should give up their home.' Stupid idea. A better idea is to increase the rents if the income goes up a lot, not throw them out!
For a start, they could easily be on low income again 5-7 years later, so what are they meant to do then, go on the housing list again, and wait another 3-4 years to be housed? What's more, most people on a low enough income to qualify for social housing, will never be on a very high income anyway.