The four boroughs forced to trial a £500-a-week benefit cap will spend their whole share of an emergency hardship fund within five months unless they move people to cheaper areas or obtain more funding.

Research by London Councils for Inside Housing reveals the four London boroughs unexpectedly having to trial the government’s £26,000-a-year benefit cap could spend their share of the pot before their peers are affected at all.

Bromley, Enfield, Croydon and Haringey councils found out on 19 December that only their residents will be hit by the cap from 1 April.

The research shows nearly 5,000 households will be affected in the four boroughs.

The councils will receive £8.16 million in discretionary housing payments in 2013/14 but the cost of ‘topping up’ rents will be £22.4 million.

If the councils were to top up rents completely, the DHPs will run out in little more than four months. The boroughs could be at a disadvantage as they will have less of their DHP money left to help house people than councils affected later on.

The real picture is likely to be worse as some of the DHP allocation is ring-fenced for other purposes, such as mitigating against the bedroom tax, which comes in from April, and local housing allowance cuts.

All four boroughs are calling on the Department for Work and Pensions to increase their level of DHPs and to reimburse them for costs.

Nigel Minto, head of housing at London Councils, said boroughs will be forced to decide whether to top up rents from their general funds or place people outside the boroughs.

He said: ‘We would not be expecting the boroughs to be making a loss purely on the basis they are introducing the cap earlier than the other authorities.’

A spokesperson for the DWP said the government could make some extra funding available. He added, however, that DHPs are not designed simply to top up rent.