A plane carrying the remains of the first eight British victims -- among them three members of one family -- arrived Wednesday at a UK military air base, where grieving relatives waited.
Patrick Evans, Adrian Evans and Joel Richards were on the first day of their holiday together when they were killed.
"We are a very small and normal family, but nothing will ever be normal again," said Richards' mother, Suzanne Richards, in a family statement.
"My son Joel, dad Pat and brother Adrian were our rocks and we are all heartbroken and devastated and will never get over losing them."
The other victims on the plane were named by the UK Foreign Office as Carly Lovett, Stephen Mellor, John Stollery, and Denis and Elaine Thwaites.
The coffins were to be taken from the air base, RAF Brize Norton, to a London coroner's office.
Tunisian authorities have stepped up security as they investigate whether the gunman they say was responsible for the attack, Saif Al-Deen Al Rezgui, had accomplices in Friday's deadly shooting at a beach hotel in Sousse.
Seven Tunisians have been arrested, Tunisian court spokesman Sofiene Selliti told CNN.
Selliti said that "very important information was found on the terrorist's phone," which was recovered from the sea near the beach where the attack was carried out.
The investigation continues, Selliti said.
Identification process ongoing
Britain suffered the heaviest loss in the attack.
UK Foreign Secretary Philip Hammond said that the number of confirmed British victims is 29.
The bodies of three Irish victims are expected to be repatriated, Tunisian Health Minister Said Aidi told CNN.
Asked why it had taken so long to identify victims, Aidi said that he did not think it had taken a long time and that authorities had to be precise and follow international procedures.
Tunisia's Foreign Ministry said that 34 bodies have been identified -- 26 Britons, one Belgian, two Germans, one Russian, three Irish citizens and one Portuguese citizen.
Aidi told CNN the remaining four victims are likely to be confirmed as British, but the identification process was ongoing.
On Tuesday, four of the most seriously wounded Britons arrived back in the United Kingdom, flown home on a military plane to receive treatment.
The gun rampage is the most significant attack against British citizens since the London transport bombings 10 years ago
ISIS claims responsibility
The possibility of a link to another Tunisian terrorist attack emerged Tuesday.
Al Rezgui, 24, trained with the people who carried out the attack on the Bardo Museum in Tunis
in March, Rafik Chelli, Tunisia's secretary of state for national security, told CNN.
In an online audio statement, ISIS -- which has said it's behind the beach resort attack -- claimed responsibility for the Bardo Museum attack and identified two men, Abu Zakariya al-Tunisi and Abu Anas al-Tunisi, as having carried it out. CNN could not independently verify the legitimacy of the audio claim.
Police shot Al Rezgui dead near the scene of Friday's attack. Authorities said he carried out the attack alone.
A man named Fathi was working on a nearby house during the attack, and he watched the gunman die.
"He was waiting for the bullet to die, like he'd finished his mission," he told CNN.
Cameron: Intelligence cooperation
Addressing the UK Parliament, Cameron said there had been successful discussions between Tunisia and Britain on security.
"This is looking at everything ... from protective security at hotels and resorts all the way through to intelligence cooperation at the highest levels between Britain and Tunisia, so we can help with their capacity to combat appalling events like this," he said.
"It is going to need a lot of long-term work between our two countries, but we also have the French and the Germans and the Americans also willing to help, and we need to coordinate between ourselves how best to support this country on its road to democracy."
Tunisia's Interior Ministry released details and images via Facebook of two more suspects -- described as "dangerous terrorists" -- it's seeking in connection with the attack.
They are identified as Rafeeq al-Tayary, 28, and Mohammed bin Abdullah bin Mohsen al-Shirady, a 23-year-old student.
Interior Minister Mohamed Najem Gharsalli announced an initial round of arrests Monday of what he said was "a first group, the important part of the network that was behind this terrorist criminal."
Appeal for hotel workers
Many tourists chose to cut short their vacation after the bloody attack at the Hotel Riu Imperial Marhaba.
Although some vacationers remain
, Tunisian officials fear that safety concerns will punch a huge hole in the tourism revenues that directly contribute about 7% of the country's gross domestic product.
One British tourist, Nathan Priestley, has set up an online appeal to raise funds
for the hotel staff whose courage during the attack "helped save so many lives that day" -- but who stand to lose out as the stream of visitors dries up.
"A lot of them have had to put on a brave face and continue to work during these tough times," he said.
They are receiving no psychological or financial support, he said, "and many of them have been told not to come in to work because there are barely any guests left in the hotel."