Firms caught paying staff less than the National Minimum Wage will be "publicly named and shamed" by the UK government in a bid to deter other businesses from underpaying workers.

The business department said it is stripping away restrictions on the naming of firms who fall foul of wage law under a new scheme which takes effect from October 2013. They will still be subject to the same financial penalties and prosecution in the most serious abuses.

"Paying less than the minimum wage is illegal. If employers break this law they need to know that we will take tough action," said Employment Relations Minister Jo Swinson.

"This is why I'm making changes so it is easier to name and shame employers who break the law. This gives a clear warning to rogue employers who ignore the rules, that they will face reputational consequences as well as a fine if they don't pay the minimum wage."

Under the current system, the government can only name businesses caught out by HMRC underpaying staff certain criteria are met, such as the amount owed to workers being more than £2,000.

"The Low Pay Commission (LPC) has been disappointed that only one person has been named under the scheme up until now, and has encouraged the government to reconsider the rules," said David Norgrove, chairman of the independent body LPC, which advises the government on the NMW .

"These changes are welcome, and to name more employers who do not pay the minimum wage should encourage greater compliance and help the low paid."

Unions also backed the move to expose dodgy firms.

"It is right to name and shame minimum wage rogues, so that other employers who think they can get away with paying illegal poverty wages get the message loud and clear that cheating does not pay," said Frances O'Grady, general secretary of the Trades Union Congress.

"At the moment all employers who have been found guilty of cheating workers out of a legal wage have to pay a financial penalty, but as this takes place behind closed doors, justice is not seen to be done."

However, O'Grady said naming and shaming is not enough and the government should go further.

"Employers need to know that there will be no hiding place if they break the law. The government must put more money into enforcement so that there are fewer places for even the most determined minimum wage cheats to hide," she said.

"We need to see more prosecutions and much higher fines imposed so that minimum wage crimes become a thing of the past."

The NMW for adult workers - those over 21 - will rise to £6.31 on 1 October.