Employers’ worst excuses for paying under the minimum wage have been revealed by ministers on the eve of a £1.7m advertising drive to encourage workers to check they are being paid the legal rate.

Underpaying bosses told officials that they thought the minimum wage didn’t apply to foreign workers; that they didn’t pay shop workers when there were no customers to serve; and in one case “she doesn’t deserve the national minimum wage because she only makes the teas and sweeps the floors”, according to the Department for Business, Energy and Industrial Strategy.

Since February 2013, the government has fined nearly 700 firms a total of £1.3m for underpayment and forced them to pay back £3.5m in missing wages. But MPs have claimed the system is not tough enough and workers have complained that bosses are often given the benefit of the doubt.

The new campaign will feature bus and billboard advertising starting next month and comes ahead of an increase in the national minimum wage for over-24s to £7.50 an hour on 1 April.

“There are no excuses for underpaying staff what they are legally entitled to,” said the business minister, Margot James. “This campaign will raise awareness among the lowest-paid in society about what they must legally receive and I would encourage anyone who thinks they may be paid less to contact Acas as soon as possible. Every call is followed up by HMRC and we are determined to make sure everybody in work receives a fair wage.”

Among the excuses heard by HMRC inspectors was a claim “the employee wasn’t a good worker so I didn’t think they deserved to be paid the national minimum wage” and “I thought it was OK to pay foreign workers below the national minimum wage as they aren’t British and therefore don’t have the right to be paid it”.

Another reportedly said: “It’s part of UK culture not to pay young workers for the first three months as they have to prove their ‘worth’ first.”

But HMRC’s role in policing failure to pay the minimum wage has been criticised by Roger Lilley, one of two newspaper delivery workers who received the biggest payout yet for breaches by Midcounties Co-op.

“Our case took over 300 days to resolve,” he said. “Our evidence did not carry nearly as much weight as the employer. HMRC were not at all on our side.”

Lilley has written to the business secretary, Greg Clarke, to complain about “yawning gaps of non-disclosure” in the investigative process and a lack of information about how the repayment had been calculated between the employer and HMRC.

A chef who worked at Le Gavroche, the Michelin-starred restaurant owned by Michel Roux Jr who was exposed for underpaying the minimum wage last year, told the Guardian that Acas encouraged him to try and settle the issue directly with his employer which he said appeared to allow bosses the chance to avoid investigation by HMRC.

The business ministry said HMRC’s enforcement budget was increased from £13m to £20m in April 2016, allowing for more compliance officers. An additional £4.3m in enforcement funding was announced by the chancellor, Philip Hammond, in November.