This a startling figure: Over 7,000 low income London families will lose over £100 a week as a result of the benefit cap, equivalent to one in three of all households affected, according to official figures.

Campaigners fear that many of these households will be unable to cope with the drastic drop in income (and as many of them have little room to cut their living costs they could be right). As a result, they fear, the families will run up rental arrears and be evicted from their home, or be forced to move into cheaper accommodation either elsewhere in the capital or further afield.

The cap is not, strictly speaking, inescapable. Households will avoid the cap if an adult member can find a job that offers at least 16 hours a week (for single parents) or 24 hours (for couples).

How many of these 7,000 families join the exodus of low income people out of the capital, then, depends largely on how ready they are for work, and whether work (or more work) is available.

I met some families affected by the cap in Tottenham in March. They told me that work was scarce or non-existent in that part of north east London. Some had part time work, but were unable to extend their hours. Childcare costs were prohibitive. Some were already homeless and in temporary accommodation, and feared being made homeless again.

Their local authority, Haringey, which is one of four London boroughs piloting the benefit cap, has pledged not to evict anyone hit by the cap for the duration of the pilot. But is worth recalling the words of Tottenham MP David Lammy, when asked at the meeting I attended whether cap victims would find themselves being made homeless:

The answer is yes … Let's be brutally honest. If in a year's time people have huge arrears, Haringey will be put in a very difficult position.

A large proportion of the households hit by the cap - there are 21,800 in the capital according to the Department for Work and Pensions (DWP) figures - are likely to be bigger families, suggesting tens of thousands of children will be affected. As the British Medical Association noted this week, this will have a dire impact on those children's health and wellbeing.

Labour's shadow employment minister Stephen Timms, whose parliamentary question dug up the figures, told me it he believed it was inevitable that many of those 7,000 families were likely to have to move out of London to find cheaper accommodation.

Poorer families may be able to muddle through if the cap took, say, £20 a week out of their pockets (around 3,000 households in the capital will lose up to £20 a week), he suspected, but £100?

These figures are very disturbing. What are you supposed to do if you lose £100 a week?

Labour voted against the cap as it stands but instead of the universal £500 a week limit would introduce regional rates, with a higher cap in London.

Alison Garnham, Chief Executive of the charity Child Poverty Action Group, said the numbers brought home the real impact of benefit cuts on families in London.

It's hard to imagine how better off families would cope with losses of £100 a week – but thousands of the poorest families in the capital are being asked to do just that.

Over 70% of those affected by these changes will be children, who will face disruption to their schooling, social networks and family support. These changes will have long term costs for their prospects, for local authorities and for central government, and do nothing to help families find the jobs and childcare they need.

The boroughs with the highest numbers of households losing over £100 a week are: Brent (900); Westminster (600); Tower Hamlets (500); Ealing (500) and Newham (400). You can see the full list here.

The work and pensions secretary Iain Duncan Smith claimed recently that the very threat of the cap had already galvanised 8,000 claimants to move into work, but this assertion was roundly criticised by the UK's statistics watchdog on the basis that it was groundless.

How dismal the impact will be largely depends on the jobs issue. Local authorities and job centres are working closely with those affected to help them into employment. But for many it will be an uphill struggle.