It looks as if Labour was intending to extend LHA to social tenancies eventually. Consider the following interchange in the House of Commons in 2004 (LHA had been tried out for a couple of years in "Pathfinder" authorities):
- (2) whether there will be a hardship payment to prevent the eviction of those tenants whose rent is higher than the new local housing allowance. [R] 
So the coalition is levelling the playing-field, as it were. Labour were as prepared to price private tenants out of too-large accommodation as they accuse the government of being in respect of council tenants.
Would Labour repeal the new arrangements? Some back-benchers seem keen, but the official spokespeople have been equivocal. Both should address the situation of private tenants.