The number of underpaid workers is at a record high with a total of £1.7m owed in back pay, according to figures from The Department for Business, Energy and Industrial Strategy.
Primark failed to pay 9,735 workers a total of £231,973, while Sport Direct failed to pay 383 workers £167,036 and Bristol Rovers underpaid 52 employees by £1,651.
The government gave out £1.3m in fines for those underpaying national minimum wage (NMW) and national living wage (NLW) rates.
Bryan Sanderson, chairman of the Low Pay Commission (LPC), said, “The LPC’s conversations with employers suggest that the risk of being named is encouraging businesses to focus on compliance".
Sanderson felt that it was “imperative” that the HMRC kept up its work to put pressure on those failing to pay minimum wage, especially in cases involving workers vulnerable to “ the most serious exploitation.”
However Bill Longe, head of employer solutions at mid-tier firm RSM, argued that naming and shaming businesses could have a detrimental effect on their reputation even if it is an “innocent error in attempting to operate a complex scheme.”
“Whilst it is absolutely right that there are sanctions in place for scoundrel employers who deliberately set out to underpay workers, the automatic naming and shaming of companies that inadvertently fall foul of the complex rules is difficult to accept,” Longe said.
“Following a routine audit by HMRC, Primark confirms it has paid a number of its employees in instances where HMRC deemed these employees to have received less than the NMW," a Primark spokesman said.
"The average amount paid per employee was £23.75 and relates to a workwear policy that was changed in 2016 and also to administration costs for court orders involving a small number of staff.
"The company is committed to the NMW and has apologised to the employees concerned.
"It has also reviewed its procedures in order to avoid this situation re-occurring," they added.
A spokesman from Sports Direct said: "This matter relates to the historical situation in our warehouse that was widely publicised in 2016, for which we apologised at the time.
"We cooperated fully with HMRC to make back payments to Sports Direct staff who were affected.
"We are committed to treating all our people with dignity and respect, and we pay above the NMW," they added.
In September, the Low Pay Commission found that women make up two thirds of those being underpaid the NLW, with research suggesting that they’re less likely to complain about it through traditional routes.