Social housing is associated with three "mobility" problems relating to tenure (people are unlikely to move out to renting or owning), size (people have homes that are too big or small for their current needs) and geography (allocation is quite localised making it hard to get housing in another Local Authority and making it hard to move). The coalition government has been talking about how to tackle these problems.
In terms of size and geographical mobility, CLG have been talking about mechanisms to encourage swaps. I am retired with a big house near the city centre, you are a working family with a small flat in the suburbs. We are both better off if we can swap. It really is hard to see why anyone should object to this, aside from the fact that it may have relatively little impact on the problem (at some point early on in economics, students learn that one of the roles of money is to facilitate exchange because it removes the need for double coincidence of wants - i.e. we both have to want to swap).
Other proposals are more tricky. For example, giving people the right to ask to move must be good from the point of view of the person asking. But, the overall effect depends on the supply of social housing in different areas. In unpopular areas it means low occupancy, while in popular areas it means excess demand. How do you square the latter with the idea that Local Authorities should be allowed to prioritise "local people"?
Similarly, removing the job market disincentives created by social housing provision (and through the housing benefit system) would seem to be very important, but changing tenure conditions may well exacerbate that problem, not mitigate it. More generally, insecurity of tenure is (at least according to the anecdotal evidence) a major cause of considerable distress to many social housing tenants. That isn't to say that you shouldn't try to tackle these issues but it does highlight how difficult is the road ahead.