P&O Cruises has cancelled all international cruises on Arcadia, Aurora, Azura and Ventura until the end of August.
Trips outside of the UK on Britannia and Iona have also been scrapped until the end of September.
P&O Cruises president, Paul Ludlow, said: “We remain in very close contact with the UK government and associated bodies as we monitor the latest situation and guidance on travel.
“From the moment we see travel restrictions lifting we will begin the significant logistical task to re-start our operations.
“It will take some time for the first ship to return to service, followed by the phased return of the remaining fleet.
“We cannot wait to welcome everyone back on board with the protection of effective protocols to safeguard the health and wellbeing of all crew and guests.”
P&O Cruises will instead offer a series of short break and week-long UK cruises this summer.
“Following recent government announcements and as the vaccine programme is rolled out across the globe, we can all begin to feel a sense of reassurance and hope that this current lockdown period in the UK will come to an end.
“Life can, we hope, slowly return to some semblance of our previous normality as hospitality opens up and summer holidays can be booked with confidence.”
He added: “While holidays here in the UK will be the first to become a reality we will, of course, gradually see the return of international travel but first we want guests to be able to enjoy a proper summer holiday at sea with the best in relaxation, entertainment and dining choice.
“These sailings will leave from our home port in Southampton and sail around UK coastal waters enjoying the summer sunshine.
“More details of dates, prices and the experience on board will be announced later this month, but they will, of course, all have flexibility so guests can book with confidence.”
The ex-UK trips will go on sale later in March.