The head of the Trades Union Congress has written to the Insolvency Service calling for it to disqualify the directors of P&O Ferries after they sacked nearly 800 crew without notice.

In a letter seen by the Guardian, Frances O’Grady, the TUC’s general secretary, said the Insolvency Service should “initiate disqualification proceedings against the directors of P&O Ferries Division Holdings Limited”.

The Insolvency Service last month confirmed it had “initiated both formal criminal and civil investigations” into the circumstances of the redundancies, after making inquiries at the request of the government.

P&O Ferries caused outrage when it fired 786 workers with immediate effect on 17 March, despite no notice or consultation with unions, as required under company law. The company, which is owned by Dubai-based DP World, instead said it would replace those workers with lower-paid agency staff.

A week later, Peter Hebblethwaite, the chief executive of P&O Ferries, admitted to astonished MPs that its directors “chose not to” consult workers despite acknowledging there was “absolutely no doubt we were required to consult with the unions”.

His testimony prompted MPs to ask whether he was a “shameless criminal”, but he insisted he would “make this decision again”.

The Insolvency Service investigation will be watched closely by the government, which has said it is unable to take direct action against the directors of P&O Ferries despite the company admitting to breaking the law.

Boris Johnson had initially promised to take legal action in the courts against the company, but a week later it emerged that this was not the case, and that the government would instead rely on the Insolvency Service investigation.

In her letter, O’Grady wrote that there were three separate legal grounds for disqualifying Hebblethwaite and his fellow directors: failing to consult unions on the sackings; failing in their duty to “have regard to the interests of their employees”; and failing to notify the flag states of the ship concerned. All three are legal duties, she said.

“The directors of P&O Ferries have knowingly broken the law and have acted against their fiduciary duty to have regard to the interests of their employees. Mr Hebblethwaite even said he would do the same again. The reputation of their company is in tatters,” O’Grady wrote.

Louise Haigh, the shadow transport secretary, said: “Months on from their shameless, criminal act, P&O bosses have faced no consequences whatsoever. The government has talked a good game but has completely failed to hold them to account.

“No ifs, no buts, the entire board should be struck off for trampling over the rule of law in this country.”

The government’s Maritime and Coastguard Agency (MCA) had subjected P&O Ferries to detailed inspections, amid concerns over possibly “inexperienced crew”. The company complained that the agency was acting with “unprecedented levels of rigour” after several vessels were prevented from sailing.

P&O Ferries is now running all of its ships between Great Britain and Ireland, Northern Ireland and the Netherlands. Only on the busy Dover to Calais route – a key UK trade artery between which ships each cross the Channel up to 10 times a day – are two of four ships still being inspected by the MCA.

Proposed legislation the government said would ensure P&O and other ferry operators pay seafarers the minimum wage was outlined during the Queen’s speech earlier in May. However, port operators and the TUC both cast doubt on whether the proposed laws would have any effect in practice.

After a public outcry over the sackings, ministers confirmed in April that DP World would lose its status as a partner in the Solent freeport. However, DP World is still listed as a “partner” on the Thames freeport. Freeports offer businesses in the area low taxes in the hope of stimulating investment, but their benefits are questioned by many economists.

The directors of the P&O Ferries holding company include Hebblethwaite and five others, one of who is listed as resident in the United Arab Emirates and another in Luxembourg.

P&O Ferries declined to comment. The government’s business and transport departments also declined to comment, and the Insolvency Service said it was unable to comment while investigations were ongoing.