The death toll of Britons killed in the Tunisian gun attack will double to at least 30 once identification of victims is complete, the BBC understands.
The Queen sent her "sincere condolences" to victims' families, saying she was "shocked" at the attack.
Meanwhile, relatives of those who are injured or still missing anxiously await news of their loved ones.
A total of 38 people were killed when a man with links to the Islamic State group opened fire near Sousse.
Tunisian officials have said they are certain 23-year-old Seifeddine Rezgui had help in carrying out the attack.
The identification of British victims is taking time because of stringent Tunisian regulations, the BBC has been told.
A senior government source said the coroner in Sousse requires medical or dental records in order to complete the formal identification process.
Home Secretary Theresa May suggested officials were having difficulty identifying the British victims as many were not carrying identification and because the injured were being moved between hospitals.
She said "every effort" was being made to ensure families were getting information that was "100% correct".
Scotland Yard said its investigation into the attack was "likely to be one of the largest counter-terrorism deployments" since the aftermath of the 7/7 bombings in London in 2005, which left 52 dead.
The Met said the operation currently involved more than 600 officers and staff, with many sent to British airports to speak to hundreds of returning holidaymakers.
It has also deployed 16 officers to Tunisia, including forensic specialists and family liaison officers.
Gunman's family held
The Foreign Office has updated its travel advice to warn that further terrorist attacks in Tunisia are possible, and urged people to be vigilant.
The Tunisian government has brought in increased security measures, with army reservists to be deployed to tourist sites.
Interior ministry spokesman Mohamed Ali Aroui said investigators were "sure" Rezgui had accomplices.
They believe the suspected accomplices provided the Kalashnikov assault rifle to Rezgui and helped him get to the scene, Mr Ali Aroui told AP.
He said the attacker's father and three friends he lived with in Kairouan, where he studied, had been detained for questioning.
The British victims have not been officially identified but the names of some have been confirmed by friends and family:
- Carly Lovett, 24, a beauty blogger and photographer from Gainsborough in Lincolnshire, who was first to be named
- Sue Davey and her partner Scott Chalkley, both in their 40s and from Tamworth, whose deaths were confirmed by their respective sons
- Adrian Evans, his father, 78-year-old Patrick Evans and nephew Joel Richards, 19, from Wednesbury, West Midlands
- Bruce Wilkinson, 72, from Goole, East Riding
- Lisa Burbidge, in her 60s, from Whickham, Gateshead
- Claire Windass, 54, from Hull, was on the beach with her husband, who survived
- Jim and Ann McQuire, from Cumbernauld, whose names were announced at their local church
- Trudy Jones, 52, from Blackwood, in Caerphilly county
- Stephen Mellor, 59, from Bodmin in Cornwall, whose death was confirmed by his wife Cheryl, who is injured and in a Sousse hospital
Three Irish people were also killed in the attack.
One Belgian and one German have been identified among the dead, the Tunisian health ministry has said, while Tunisians are also thought to have been killed.
At least 36 people were injured, some seriously.
Buckingham Palace earlier released a statement from the Queen saying: "Prince Philip and I were shocked to learn of the attack on British tourists in Tunisia on Friday.
"We send our sincere condolences to the families of those who were killed and our deepest sympathy to the people who are still fighting for their lives in hospital, and those who have been seriously injured.
"Our thoughts and prayers are with those of all countries who have been affected by this terrible event."
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Holiday firms have put on extra flights on top of scheduled services for people wanting to return home. Flights to the country have also been cancelled.
Tour operator Thomas Cook laid on two extra flights on Saturday and one on Sunday.