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.
More top news
The test screens for eight common forms of cancer and helps identify the location of the disease.
New Zealand's recently elected prime minister has announced that she is pregnant.
Top temperatures only reaching 7 Celsius (45 F).