Tenants with one spare bedroom have had a payment reduction of 14% and those deemed to have two or more spare a reduction of 25%.
Lawyers for the 11 cases say that, unless the families move from their homes into smaller properties, they face building up rent arrears and being forced out any way.
More top news
David Cameron sets out his case for British jets and drones to strike so-called Islamic State targets in Syria in an address to the Commons.
A drink-driver who "destroyed the lives" of two mothers was allowed to have his curfew lifted so he could go on a foreign stag party.
Demonstrators have blockaded the entrance tunnel to Heathrow Airport in apparent protest at plans to build a third runway.