The former MasterChef host Michel Roux Jr has begun reimbursing staff who were paid less than the legal minimum wage at his £212-a-head Mayfair restaurant.

Current and former chefs at Le Gavroche are in line for payments running to thousands of pounds each after a Guardian investigation last month exposed Roux for paying kitchen staff, who worked up to 68 hours a week, as little as £5.50 an hour. The wages worked out at well below the £7.20 legal minimum for people aged over 24.

Roux has now written personally to former chefs apologising for their underpayment and promising to make up shortfalls in their pay. He has also sent four-figure cheques to others, which are arriving just in time to fund an upgrade from Christmas Day cava to champagne for some of his hard-pressed former workers.

Roux wrote: “It has been brought to my attention that some ex-staff may have been underpaid and this may affect you. If this is the case then please accept my apologies and reassurance that this was not intentional.” He asked former staff to “confirm any shortfall that may be due”.

A spokeswoman confirmed that letters had been sent out and said: “Of the people he has been in contact with in the kitchen team, he will settle with everybody who feels they have a legitimate claim and he will honour it.” Roux now faces a bill running into tens of thousands of pounds. One former chef told the Guardian he will tell Roux he is owed close to £8,000.

Another former chef quoted from Charles Dickens’s A Christmas Carol in describing Roux’s repayments as “a fair, even handed, noble adjustment of things”. “But,” he said, “it was an adjustment of an unfair, underhanded and ignoble practice in the first place and it was forced. These issues will persist in the restaurant industry unless they are challenged by staff and the public.

“It is not OK. Chefs and waiters should expect to be paid at least that required by law and customers should be confident staff are well treated.”

The move came exactly a month after Le Gavroche chefs blew the whistle on their low pay. They revealed that while they were preparing dishes such as the £60.80 butter-poached lobster with almonds, peas and a bisque sauce for guests including Paul McCartney, Adele and the Queen, they were working between 62 and 68 hours a week for £375 before tax.

It was described as “simply not acceptable” by the Sustainable Restaurant Association, led by rival Michelin-starred chef Raymond Blanc. One former chef at the restaurant said that while Roux was in many ways a supportive employer, the pay was “disgusting”.

Roux’s friends, meanwhile, rallied to support him. They included the restaurant critic Jay Rayner, who said that while underpayment of the minimum wage was wrong, Roux was “not quite the anti-Christ” and was “a good employer”. Rayner said the problem of underpayment in the restaurant industry was “systemic”.

Roux had said that despite being hands-on at the two-Michelin star restaurant, he had not noticed the long hours some of his kitchen staff were working and said “in no way was it done intentionally”.

Some chefs are understood to have been wary of approaching Roux directly to ask for missing pay for fear that such a move could affect their career prospects. Roux is an influential figure in the UK restaurant industry, with numerous former Gavroche chefs running top kitchens. They include Gordon Ramsay, Marco Pierre White and Marcus Wareing. But Roux appeared to head off any such fears, saying requests for back pay would be handled confidentially by his restaurant’s payroll department.

“I think it is brilliant he has done this,” said one former chef who is preparing to lodge a substantial request for back pay. “It would be nice if other restaurants did the same, as I am sure many others are paying beneath the legal minimum.”

Underpayment of the minimum wage is punishable by a fine levied by HMRC, and last night Frank Field MP, chairman of the House of Commons work and pensions select committee, called on Theresa May to order HMRC to investigate Le Gavroche.

“What better opportunity for the prime minister to offer low-paid workers some Christmas cheer?” said Field. “If Mrs May were to ask HMRC to identify all of the staff who were underpaid by Le Gavroche, and order that they be repaid their lost earnings, other high-end restaurants might think twice before ripping off their own staff.”

Last week the Guardian also revealed that Le Gavroche has been keeping all the discretionary 13% service charge it levies on customers bills and does not distribute it to staff on top of their wages. Roux responded by abolishing the charge and increasing prices by 13%. He said this would clear up any ambiguity about what the service charge was for.

On Friday he tweeted: “Never touched tips in my life, every penny goes to staff without anything withheld. All SC [service charge] goes to wages, not a penny creamed off either.” He recently changed his Twitter avatar to an image of one chef punching another.

His tweet appeared to foster more confusion, with several people saying service charges shouldn’t be used to pay wages. Roux defines tips as cash or card payments over and above service charge which he has treated as restaurant “revenue”.