Protests are taking place at Dublin Port and a number of UK ports over the sacking of hundreds of seafarers, as calls grow for a P&O Ferries' boss to quit.
New Labour leader Ivana Bacik said what happened at the company shows the need to strengthen workers and union rights.
She said what P&O had done was "bad practice" and she called on the company to reverse its decision.
The demonstrations come after a ship operated by the ferry firm was detained for being "unfit to sail".
The European Causeway vessel has been held at the port of Larne due to "failures on crew familiarisation, vessel documentation and crew training", the Maritime and Coastguard Agency said.
British Transport Secretary Grant Shapps said he will not compromise the safety of P&O vessels and insisted that the company will not be able to rush training for inexperienced people.
In a move that sparked widespread outrage, the company sacked almost 800 seafarers earlier this month, and plans to replace them with agency staff on cheaper salaries.
A spokesperson for the Maritime and Coastguard Agency said: "We can confirm that the European Causeway has been detained in Larne.
"It has been detained due to failures on crew familiarisation, vessel documentation and crew training.
"The vessel will remain under detention until all these issues are resolved by P&O Ferries. Only then will it be reinspected."
The MCA said there were no passengers or freight on board the European Causeway vessel when it was detained.
The detention of ships is based on concerns over their safety and to prevent them going to sea.
Protesters gathered in Liverpool, Dover and Hull as the RMT union urged a stop to the "P&O Jobs Massacre".
The Trades Union Congress tweeted a video it said showed P&O dockers in Rotterdam refusing to load freight onto a ferry set for Hull "in solidarity with the 800 seafarers illegally sacked by P&O".
The Labour party has written to Business Secretary Kwasi Kwarteng asking whether the government will seek the removal of P&O Ferries' chief executive Peter Hebblethwaite as a director under the Company Directors Disqualification Act 1986.
In a letter, the party accused the government of "sitting on their hands" rather than taking action to hold P&O to account, adding that the "toothless response risks giving the green light to exploitation".
Shadow transport secretary Louise Haigh said the "shameful misconduct of P&O Ferries has ruined livelihoods" as she called for the sacked workers to be reinstated and for Mr Hebblethwaite to be "barred" as a director for his role in the crisis.
British Prime Minister Boris Johnson backed Mr Shapps' call for Mr Hebblethwaite to quit.
In Larne, the local mayor of the Mid and East Antrim Council, William McCaughey, said they would support the reinstatement of the staff immediately.
"It is ridiculous what P&O has done to the staff, we in Larne would be very keen to see staff reinstated, it is the least that P&O could do," he told the PA news agency.
The RMT union said it welcomed the detention of the European Causeway and it demanded the Government "seize the entire fleet" of P&O vessels.
SIPTU is also staging a rally outside the P&O terminal in Dublin Port.
SIPTU organiser Jim McVeigh described the company's actions as despicable and he said the union wants to see staff reinstated in their positions.
"This has really angered people across these two islands because people know if we let them away with that there you could be next, I could be next, someone just could come in and say pack your bags and get off the premises. That's not the way we should operate anywhere."
Mr McVeigh also said the impounding of the P&O ferry in Larne was a positive development.
About 30 people, including P&O workers, who gathered at the entrance to the terminal received lots of support from passing motorists.
Additional reporting Samantha Libreri
