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.
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A four-year-old boy has died after being hit by a car outside a medical centre in Leeds.
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The US President has marked his first 100 days in the White House by speaking at a campaign-style rally in Pennsylvania.