A single mother-of-five who was made homeless after resisting Westminster Council’s attempt to move the family 50 miles from the capital is applying to the Supreme Court to review her case.

Titina Nzolameso is a British citizen who has lived in London for 16 years and her children have been settled in schools in Westminster for the past five years. They were forced to leave their four-bedroom flat in Westminster after the introduction of the benefit cap meant housing benefit no longer covered the rent.

The benefit cap ensures that no family can receive more than £500 from the state in a week, including all housing costs. For families in London and other high-rent areas, this puts even social housing beyond the means of many, and experts say the policy is “cleansing” the capital of its poorest residents.

In November 2012 Ms Nzolameso applied for cheaper housing in Westminster, but instead the council offered her accommodation near Milton Keynes, 50 miles away. When she turned that down, the council said it no longer had a duty to find her a home.

Her children Tasnim, 14, Hussain, 13, twins Jamilah and Amirah, 10, and Daliya, 9, have all been placed into foster care until the family has a permanent home. The situation means Ms Nzolameso is sleeping on friends’ sofas and is able to visit her children only at set times three days a week.

“It’s wrong what they’re doing,” Ms Nzolameso said. “London is our home and my children don’t want to move to Milton Keynes. It would disrupt their education.”

“It would either mean a two-hour commute to get my children to school in Westminster, or they would need to be uprooted to new schools in Milton Keynes, an area I have no local connection to whatsoever. There was no evidence to suggest that Westminster had even looked to find me accommodation nearby.”

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If she were to leave the capital, Ms Nzolameso is also concerned about losing the network of friends that support her and help out when she is unwell. She suffers from depression, diabetes and high blood pressure.

The family came to Britain from the Democratic Republic of Congo in 1998 and claimed asylum. Ms Nzolameso now has British citizenship. She separated from her children’s father in 2007 but they still have contact with him, although this too would be harder if they moved to Milton Keynes

Ms Nzolameso’s case was turned down by the Court of Appeal last week and her lawyers told The Independent that they now plan to take it to the Supreme Court.

Her solicitor, Jayesh Kunwardia, said: “This judgment could have dire consequences for vulnerable families across the country. It gives the green light for councils to engage in social cleansing of the poor on a mass scale. Council tenants are being threatened with homelessness unless they agree to uproot themselves from communities they’ve lived in for years”.

Rejecting the case last Wednesday, Justice Moore-Bick said: “I accept that the court should be astute to ensure that local housing authorities...do not merely apply policies which lead to accommodation being provided outside their own districts in a routine and unthinking manner. On the other hand, many authorities, of which Westminster is one, are under great pressure to discharge their statutory obligations and should not be prevented from making sensible use in an orderly way of the housing stock available to them, whether within or outside their own districts.”

Of all the families affected by the benefit cap, 49 per cent are in London because of the high housing costs.

Daniel Douglas, a homelessness specialist at the magazine Inside Housing, said: “Out of area homeless placements create havoc for tens of thousands of families and children. They also set off a domino effect, where councils with bigger budgets place families in comparatively cheaper areas, meaning that the councils in these areas themselves can’t find housing for homeless people, and have to place their families in another area. At the end of this line of dominoes, the most deprived areas of the country are overwhelmed with the influx of vulnerable homeless families. A side effect of this policy is social cleansing on a shocking scale.”