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 in Northern Ireland due to “failures on crew familiarisation, vessel documentation and crew training”, the Maritime and Coastguard Agency (MCA) said.
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 in 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.”
P&O sackings: PM backs calls for ferries chief to quit
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 about their safety and to prevent them going to sea.
On Saturday, protesters are gathering in Liverpool, Dover and Hull as the RMT union urged to stop the “P&O Jobs Massacre”.
The Trades Union Congress (TUC) tweeted a video they 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”.
Labor 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.
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.
Alliance East Antrim MLA Stewart Dickson welcomed the impounding of the ferry as a safety measure.
“It’s not like the crew of an airplane getting off one Easyjet and getting on to the next one where the controls are the exactly the same, and everything is in the same place,” he told PA.
“No two ships are the same, and you cannot just fly a crew in and expect them to be able to sail a ship.”