Passengers took the decision to swim to a nearby island after becoming stranded in the early hours of Saturday, and were forced to drink their own urine and eat leaves to survive.
They were eventually rescued the following day after managing to flag down a passing boat with their life jackets. Ten survivors were rescued, including passengers from Germany, France, the Netherlands, New Zealand and Spain, as well as the holidaymakers from Britain, who are being treated in hospital. However, 10 foreigners and five crew members are still missing, with the Foreign Office saying more Britons may be among those unaccounted for.
French victim Bertrand Homassel told how he and the other passengers decided to take action after struggling
to remain afloat for almost 12 hours. He said: "Six people were in the lifeboat. The others climbed onto the roof of the boat, which had not completely sunk.
"We waited until midday on Saturday. We were five kilometres [three miles] from the coast - there were many big waves separating us from the coast.
"People started to panic … Everyone took the decision to swim to the closest island, five kilometres away, where there was an erupting volcano."
Mr Homassel described how they swam for six hours and arrived at the island, Sangeang, as the sun was going down.
The group spent the night there, fearing the worst, before being rescued the following day.
The Frenchman added: "I was really very lucky."
The vessel sank as it travelled from the island of Lombok, east of Bali, to Komodo Island.
Indonesian officials said it was believed the boat was thrown onto a reef in rough seas and sank very quickly as it made the journey between the islands, which usually takes three days. However, Mr Homassel claimed the boat began sinking slowly after its hull was damaged in the storm.
A search is still under way, with tourist vessels and local fishermen scouring the area for further survivors.
A spokeswoman for the Foreign Office said: "We are aware that two British nationals have been hospitalised following an incident in West Nusa Tenggara, Eastern Indonesia. We are providing consular assistance."
She would not comment on the injuries suffered by the two Britons.
Local police have refused to release the names of those involved in the incident until identity is confirmed.