He said it had not been an easy situation and ministers needed to "learn the lessons".
It follows criticism of the government's response to the crisis.
A plane chartered by oil companies for employees, with 78 passengers, has arrived at Gatwick and a government-chartered flight has also left Libya.
The prime minister said: "Of course I am extremely sorry. They have had a difficult time. The conditions at the airport have been extremely poor."
A flight chartered by oil companies arrived at Gatwick at about 0715 GMT.
The airport said the plane carried 78 passengers. Earlier reports suggested more people had been on board.
A government-chartered flight, which left Tripoli at 0745 GMT, is now on its way back to the UK with a stop-over in Malta.
It is expected to land in the UK in the early evening.British nationals have started to arrive home from protest-hit Libya
A RAF Hercules C130 aircraft is also expected to return to the UK later with dozens of passengers. A second military plane is on standby in Malta if needed.
The Foreign Office said "a number of additional planes" could be sent to Libya throughout the day.
Meanwhile, the Ministry of Defence has confirmed that Royal Navy frigate HMS Cumberland is now at the entrance to the harbour in Benghazi.
It will help with the evacuation process if needed.
A meeting of Cobra, the government's emergency planning committee, is being chaired by Foreign Secretary William Hague.
Helena Sheehan, 66, one of the passengers who landed at Gatwick earlier, said she had just experienced "some of the worst hours of her life".
"Libya is descending into hell," she said.
"The airport is like nothing I've ever seen in my whole life. It's absolute chaos. There's just thousands and thousands of people trying to get out."
The British Red Cross has deployed a team of volunteers to Gatwick airport to provide support to Britons being evacuated.BBC security correspondent Frank Gardner said an SAS contingent has been put on standby for emergency deployment to parts of Libya, backed up by paratroopers of the Special Forces Support Group.
Our correspondent said: "With the situation for some British nationals in Libya fast deteriorating, it's part of a range of options being considered by the government to rescue those stranded in the North African country.
"Exact numbers and the locations of any staging areas are being kept secret but it's a scenario that British Special Forces have trained hard for - landing in the midst of a dangerous and chaotic situation then securing the safe passage out of stranded Britons, all hopefully without a shot being fired."
Several other countries, including France, Russia and the Netherlands have already evacuated some of their citizens.
UK nationals wishing to register an interest in flights out of Libya should call the following numbers: 020 7008 0000 from the UK or 021 3403644/45 from Libya.
The Foreign Office is advising against all but essential travel to Libya.
Around 3,500 Britons had been living in Libya before the crisis but most of those are thought to have left in recent days.Passengers landing at Gatwick expressed relief to have left Libya
However, there is particular concern for some British oil workers thought to be stranded in isolated desert camps.
They are struggling to make contact because the phone networks have been disrupted and their supplies of food and water from Libyan cities are running out.
"Some we know have been subjected to attacks and looting. They are in a perilous and frightening situation," said Mr Hague.
After a week of upheaval in Libya, protesters backed by defecting army units are thought to have almost the entire eastern half of Libya under their control.
The country's beleaguered leader Colonel Muammar Gaddafi, who has been in power for 42 years, has vowed to fight to his "last drop of blood" rather than leave the country.
Earlier, Mr Hague told the BBC the "odds were stacking up" against Col Gaddafi, adding: "We have a government, or the remnant of a government, here which is prepared to use force and violence against its own people."
He said the Libyan leadership will be "held to account" for crimes against its people.
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