The Government has been accused of understating the number of council tenants who have been wrongly hit by the so-called 'bedroom tax' changes to housing benefit.

Last month the Guardian revealed one in ten people in Waltham Forest affected by the changes to support had wrongly had their benefits cut.

Now Labour said local authority data showed that, as a result of a loophole in the legislation, at least 16,000 households across the country had been affected in the same way - while the true figure could be closer to 50,000.

Work and Pensions Secretary Iain Duncan Smith has previously told MPs that between 3,000 to 5,000 tenants were thought to have been affected by the error.

But after submitting Freedom of Information requests to all 346 local authorities in the UK, Labour said responses from the 140 councils which have so far replied showed that 16,450 households had been incorrectly caught.

Shadow work and pensions minister Chris Bryant said that if there was a similar rate of wrongful deductions across the whole country, the final total would be almost 50,000.

"Iain Duncan Smith told Parliament that 3,000 to 5,000 people had been illegally charged the bedroom tax thanks to the loophole, but it's now clear he was just picking numbers out of thin air," he said.

"The bedroom tax has been a fiasco from start to finish and now the Government have been caught out trying to downplay how many people are exempted by it.

"This would be a farce if it weren't for the upset this has caused many vulnerable families and the huge cost to taxpayers."

Under the Government changes to the welfare rules, social housing tenants who are deemed to have more rooms than they need are liable to have their housing benefit cut, removing what ministers call the "spare room subsidy".

However, as a result of a loophole in the legislation identified earlier this year, it does not apply to certain tenants renters who have lived in the same home for more than 17 years.

Waltham Forest Council said it had started to re-assess those affected.

The Department for Work and Pensions said the regulations were now being amended and that it still believed its earlier estimate of the numbers affected was correct.

A spokesman said: "We expect very few people to be affected by this - around 5,000 - and are working with councils to ensure affected claimants are kept informed.

"The removal of the spare room subsidy means we still pay the majority of most claimants' rent, but the taxpayer can no longer afford to pay the £500 million cost of claimants' extra bedrooms."