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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Parents in Anglesey, North Wales, will have to show birth certificates in order to prove their child's age and qualify for the scheme.
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