Scuba Travel, the tour operator for the trip, said the families of the deceased had been contacted by the Foreign and Commonwealth Office.
Twenty-six other people, including 12 Britons, were rescued from the boat called Hurricane.
Initial reports suggest the fire started after an electrical fault.
The British nationals rescued are being supported by the Foreign Office.
The boat left Port Ghalib on June 6 and was due to return on Sunday.
Scuba Travel said the missing three passengers were not on the boat for the briefing and were not part of the dive plan for that morning.
The 12 divers present at the briefing were immediately evacuated, followed by the 14 crew members after attempts to reach the missing guests were unsuccessful.
Scuba Travel said it had been working with the boat's operator, Tornado Marine, since 2001.
The rescued guests were brought on shore to the village of Marsa Shagra and provided with medical assistance.
A full investigation into the fire is planned by local authorities.
LONDON DAILY ARCHIVE
Three British Tourists Die in Red Sea Boat Fire, 26 Others Rescued
Three British tourists have died after a fire on a dive boat in the Egyptian Red Sea.
12 June 2023 · 14:13 UTC
