The company said its 14 liners had been virtually full in the first three months of the year, despite a dramatic increase in capacity.
Shares in P&O rose by 52.5p to 978p as the company said that the ships in its US business, Princess Cruises, were 98 per cent full even though capacity was up by 44 per cent. The extra space includes the world's largest cruise ship, the 2,600-berth Grand Princess, launched two years ago. The outlook is also promising for the rest of the year, P&O said, with the majority of berths already booked. Cruises to Alaska and the Caribbean are proving to be popular choices.
P&O's European cruises have also been virtually full, although the company said there had been some cancellations from American passengers nervous of taking Mediterranean cruises during the Balkan crisis.
P&O's passenger-berth days - the standard measure of cruise line capacity - was 1.44 million for Princess Cruises and 359,150 on European-based P&O Cruises, the company said. P&O Cruises UK also kept up its bookings, although capacity on the cruises increased only slightly.
Of P&O's 14 cruise liners, nine are US based and operate under the Princess brand. Three are based in the UK and one in Australia, which operates under the P&O name.
Analysts said the trading update was "extremely encouraging", leading several sector watchers to upgrade their stance on the stock. "It's a good statement in every respect," said Alistair Gunn from Credit Lyonnais.
P&O announced last month that it was to raise around pounds 2bn from a disposals programme that includes selling its property interests, floating its Bovis construction business and selling the Earl's Court Olympia exhibition centre. Lord Sterling, the chairman, said the future of the group would be in cruises, ferries, ports and logistics.
At 31 December, the cruise division of the company accounted for almost one-third of the group's net operating assets.