Cameron sent security officials and government ministers to the scene and promised to intensify the fight against extremism in Britain.
The attack was the deadliest in Tunisia’s recent history.
In concrete policy terms, Cameron’s reaction was cautious, and he didn’t promise any immediate antiterrorism measures at home or any increase in Britain’s military involvement in fighting Islamic State militants.
The gunman chased the 39-year-old tourist Chris Callaghan and shot in her leg, shattering her right femur.
Tunisian authorities have arrested a group of suspects associated with him, the interior minister said on Monday without giving a number or details on links.
However, the United Kingdom Daily Mirror newspaper quoted five Britons who were caught up in the attack as saying they had seen a second attacker, who two described as wearing different coloured shorts to Rezgui.
Britain is pressing Tunisian authorities to allow rapid access for its experts dispatched to help identify bodies.
Rezgui, a Tunisian student disguised as a tourist pulled out a Kalashnikov assault rifle hidden inside a beach umbrella and opened fire on holidaymakers at the seaside hotel.
Beyond those practical steps, Cameron cast his response in terms of a battle of ideas. “We stayed there until all the firing had stopped and the whole place was surrounded by police officers, military and helicopters”.
It was the largest British loss of life in a terror attack since 52 people died in suicide bombings on the London transport system on July 7, 2005.
He said the government was working “as fast as we can” to get information to those families still waiting for news of their loved ones, three days after Friday’s attack.
He was also said to be grinning and ignoring pleas to stop the attack. Thirty of those injured were treated and released, it said, while nine remained in care. The ministry said 33 of the 38 victims have now been identified, also including 3 Irish, 2 Germans, a Belgian, a Portuguese and a Russian.
Home Secretary Theresa May is travelling to the north African nation for talks on the extremist threat and to offer condolences for the slain tourists. “They will train there and they will come back without any problem from the police”.
Those being returned include Mr Stollery, 58, a social worker from Nottinghamshire who was on holiday with his wife Cheryl, Mr Thwaites, a ex- Birmingham City football player and wife Elaine, and engineer Mr Mellor, from Bodmin in Cornwall, who was killed as he shielded his wife on the beach.
The Foreign Office has updated its travel advice to warn that further terrorist attacks in Tunisia are possible and urged people to be vigilant.