A third of disabled applicants have been refused support from a government fund designed to give them temporary financial help to cope with cuts to their benefit income as a result of the bedroom tax, a survey claims.

Ministers have persistently rejected arguments that the bedroom tax discriminates against disabled people by arguing that the availability of discretionary housing payment (DHP) grants to vulnerable households fulfils their duties under equality laws.

But a survey of councils by the National Housing Federation found that 29% of disabled people affected by the bedroom tax were turned down for help in the six months from April, and in some councils less than three in 10 disabled applicants were successful.

Separate research has found that disabled people who were refused a DHP cut back spending on living essentials such as food, utility bills and transport in order to meet bedroom tax shortfalls averaging between £11 and £22 a week.

Although ministers this year created a specially ringfenced £25m fund to help affected tenants who lived in properties especially adapted for their disabilities, just 14% of disabled applicants got DHP help in Shepway district council in Kent, the federation survey found. Less than 30% of disabled applicants succeeded in North East Derbyshire, Basildon, Rotherham and South Ribble in Lancashire.

Of the 99 English councils who responded to the NHF questions on DHP success rates, 25 replied that 100% of disabled applicants had received DHP help, suggesting that the chances of receiving financial help vary widely depending on where you live.

According to government estimates, 420,000 disabled people are affected by the bedroom tax.

The National Housing Federation chief executive, David Orr, said: "Whenever ministers are challenged on the bedroom tax, they tell us vulnerable people are not at risk because of these discretionary housing payments. But many disabled people and vulnerable families are facing miserable odds of getting help.

"Even those who are lucky enough to get support will have to reapply time and time again, each time facing the stress and worry that the funds will be withdrawn, while councils are being inundated with applications."

A spokesperson for the Department of Work and Pensions (DWP) said: "We more than tripled the money we give to local authorities to £190m this year to ensure that help was available to those who need it most.

"The cash was given to local authorities to distribute because they deal with their customers on a day-to-day basis and are best placed to see to it that the money reaches those who have the greatest need. We will continue to monitor progress closely while our reforms bed down."

In July a judge rejected a judical review claim that the bedroom tax was discriminatory on the grounds that the existence of the DHP showed that the DWP had recognised the additional needs of disabled tenants. The decision is being appealed.

Overall, 70% of all people affected by the bedroom tax who applied for a DHP in the first six months of 2013-14 received one, although there were wide geographical variations. In Redcar & Cleveland the equivalent figure was just 23%. In Wandsworth it was 30% and Wokingham 33%.

The survey found that DHP applications had increased most in the north-east of England, up 482% on 2012. The region is one of the worst hit by the bedroom tax, which withholds a proportion of housing benefit paid to working age social housing tenants deemed to have too many rooms for their needs.

DHP funding is supposed to help smooth the introduction of the bedroom tax, the household benefit cap and housing benefit cap. The DHP funds are not large enough to meet the housing benefit shortfall incurred by every affected tenant, and councils are expected to use their discretion to target payments "within priority groups". Government Guidence on DHPs states that councils "have a duty to act fairly, reasonably and consistently".

According to the survey, the most common reason for applicants being turned down (50%) is that the council considers the applicant could meet the shortfall by drawing on personal savings. A third of applicants were turned down because the council considered they would be able to cover the benefit shortfall "if they cut back on other expenditure".

Although ministers have told councils to disregard disability living allowance payments in any assessment of income, campaigners believe some councils have wrongly forced disabled applicants to use this income to meet housing benefit shortfalls.

DHPs are time-limited to just a few months, and critics say they will not solve long-term dangers of debt, rent arrears and eviction where tenants cannot meet benefit shortfalls but are unable to increase their income or move to smaller properties.