Any employer who fails to pay staff the minimum wage of £6.31 an hour from October will be publicly shamed and then hauled before the courts if they refuse to make up the arrears, amid growing pressure on government to act on the scandal of low pay.

Business secretary Vince Cable will announce within weeks that rules are to be changed from the autumn. He will probably say that ministers no longer have to be satisfied that an offence was deliberate or the result of negligence; it will be enough that an offence has taken place.

Offenders will then be named on government websites, and taken to court unless they pay the amounts owing to staff.

The move comes amid criticism of the government's failure to act on low pay, and as Labour plans to make the interconnected issues of living standards, low earnings and immigration centrepieces of its campaign for the 2015 general election.

If successful, the changes could mean windfalls for hundreds of thousands of workers who have been paid at below the minimum wage rate.

The Annual Survey of Hours and Earnings for the Office for National Statistics estimates that about 287,000 workers were paid at less than the minimum wage in 2012, while the TUC puts the figure closer to 350,000.

The business secretary told the Observer that if government was not enforcing the minimum wage, the point of it would be undermined. "Paying any less than the minimum wage is illegal, and the government takes this very seriously. Employers need to understand that they will be investigated and prosecuted if they flout the law. Workers need to be confident that they'll be supported if they make a complaint. We are simplifying the criteria and making it easier to prosecute."

Inside government there is concern that rules on punishing minimum wage offenders have been drawn too narrowly, with officials having to show that breaches were deliberate or the result of poor management before action could be taken.

Previous plans, announced in 2010, to "name and shame" minimum wage offenders have so far led to only one case being highlighted – a hairdresser from Leicester who paid a member of staff £342 for 20 weeks' work when she was supposed to receive at least £3,703.

Unions, Labour and low pay groups have also criticised the fact there have been no prosecutions for failure to pay the minimum wage for more than two years – despite evidence of around a quarter of a million people receiving below the statutory rate.

While the coalition was buoyed last week by news that the economy grew at 0.6% in the last quarter, ministers are aware that the real challenge ahead of the 2015 election will be to persuade working people that their living standards are no longer declining.

Cable is also understood to be looking at measures to protect vulnerable groups of workers, including tens of thousands of care workers, who are often not remunerated for the many hours they spend every week travelling between clients.

Labour, which is calling for the maximum fine of £5,000 for minimum wage offences to be doubled to £10,000, argues that big companies often tempt foreign workers to the UK by including accommodation, often of a very low standard, as part of their "pay packages". This then means that immigrant workers are paid at rates that undercut the levels that British workers would be prepared to accept.

From 1 October, the minimum wage will increase by 12p to £6.31 an hour for those aged 21 and over, while for 18-20-year-olds and 16- and 17-year-olds it will go up by 5p to £5.03 an hour and by 4p to £3.72 an hour respectively.