It comes after the budget airline began offering long-haul flights from the UK to the US earlier this year.
The airline, which started in 2003, was scheduled to begin a new Manchester to Malaga route later this month.
Most of the airline’s business involved taking Scandinavian holidaymakers to destinations such as Spain, Greece, Italy, Egypt and Turkey.
The Danish-registered airline is not part of the Civil Aviation Authority’s ATOL Protection scheme, which covers only passengers booked on package holidays.
Passengers who have travelled on an outward Primera flight have been advised that they will need to make their own arrangements to return to the UK.
People who had booked directly with the airline on future flights will not be covered either, the CAA advises.
Passengers who paid by credit card may be protected by Section 75 of the Consumer Credit Act 1974 and are advised to check with card issuers. Similar cover may apply if a Visa debit card was used.
Scores of customers have taken to social media to say they or their relatives are stuck in Spain.
Sally James said: “Stranded in Malaga as our flight has now been cancelled for Monday 8 October. Will have to try and get other flights home.”
Antony Meadley said: “My daughter Catherine is now stuck in Spain. She flew out on Saturday and was due to come back this Thursday.”
Primera failed to compete with other budget juggernauts like Norweigan and Wow.
Red flags began to be raised when it announced short-haul flights from Birmingham to seven European destinations would end on September 3.
It also blamed the late arrival of new aircraft from Airbus that forced it to cancel flights and lease planes.
It had planned to start flying from Madrid to New York, Boston and Toronto next month from €149 each way.