Tunisian authorities have so far confirmed eight Britons among the 38 killed yesterday. The UK Foreign Office has put the number at five but warned that the death toll could rise.
Tunisian Prime Minister Habib Essid said the "majority" of the dead were British, hours after UK foreign secretary Philip Hammond said a "high proportion" of casualties would have been British.
Cameron, speaking in Downing Street after chairing the emergency Cobra meeting to look at the UK's response to the attacks, said he could only imagine the "pain, and anguish and agony" of families caught up in these "terrible events".
He called the attack "savage" and said a "full deployment team" of consular staff, police and Red Cross experts would soon arrive in Tunisia.
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Cameron also called on the British people to work together with the authorities to "combat this poisonous narrative of Islamist extremism that is radicalising too many young minds in our country", saying the "terrorists will not succeed".
"These terrorists murdered them because the terrorists oppose people and countries who stand for peace tolerance and democracy wherever they are in the world. But these terrorists will not succeed," he added.
Tunisians, Britons, Germans, Belgians, French and at least one Irish citizen were among those killed when a gunman opened fire on tourists yesterday, responsibility for which was later claimed by the Islamic State (IS) terrorists.
Yesterday's was the biggest loss of British life from a terrorist incident since the July 7 bombings in London in 2005, when 52 people were killed.
A number of Britons have issued desperate pleas for information about relatives who have not made contact since the attack.
Thomson and First Choice said their customers were among "a number of fatalities", and they had sent 10 planes to bring 2,500 tourists back to the UK.