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 10 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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Portman was due to receive the award in Israel in June and said that her reasons for skipping the ceremony were solely due to Mr Netanyahu.
Analysis of Department for Work and Pensions data found the average man receives £153.86 a week and the average woman receives £125.98.
The country says it is making the move to shift its national focus and improve its economy.