Eastern Bali's miles of palm-fringed beaches and crystal clear seas have helped make it a paradise for water sports enthusiasts from around the world. That is what Jeremy Hoyland thought when he set out with friends in October to jet-ski between his resort at Tanjung Benoa beach and a nearby tropical islet.

Now nearly three months on, nothing has been heard or seen of Mr Hoyland, 41, who had two children, after he used his mobile phone to report engine trouble as he became separated from his fellow skiers returning from the exotic excursion. But his family refused to give up hope and set out again last night to continue their search, desperately hoping that he may still be alive, stranded on an uninhabited Indian Ocean island.

One theory is that Mr Hoyland, a highly experienced power-crafter who had gone out to Bali to act as race director for the jet-ski sports event in the 2008 Asia Beach Games, may have drifted in the region's notoriously powerful currents. While it is possible the powerful swimmer may have been swept out into the deep ocean towards Australia, the seas off the Bali and Java coasts are dotted with hundreds of small islands.

Here, there is said to be enough fruit and fresh water to survive on. Many are inhabited but locals have no means of communicating with the outside world, and the family is said to be optimistic after hearing reports of divers turning up weeks after going missing in the region.

Jacqui Holland, who is going to Bali to lead the search, said she would "leave no stone unturned". After a meeting with the Indonesian ambassador in London, Yuri Octavian Thiamin, she said she was encouraged by his support and the offer of boats and expertise. "He definitely shares our optimism that Jeremy may be alive on an uninhabited island," she said. "Ultimately we have to find something because it's so difficult for us. We can't do anything with our lives and get on with our lives without knowing."

There is also a glimmer of fresh hope. Phone records obtained through the British mobile companies Virgin and Vodafone showed Mr Hoyland had made calls for help from about three miles off Bali, near Lembongan island, his destination that day. The new hunt will focus on this area, some 15 miles from the initial search area.

Mrs Hoyland will be accompanied by her brother-in-law Nicholas and a liaison officer from South Yorkshire Police. They also engaged the services of Clarence Mitchell, the former BBC royal correspondent who has dealt with media relations for the McCann family, as well as Fiona MacKeown, whose daughter Scarlett was murdered in Goa, and the parents of Jimmy Mizen, stabbed to death in London.

The family says it will spend whatever it takes to find the missing jet-skier and has raised money with a charity concert at his daughters' school. The family has been inundated with support from around the world by jet- skiers after they set up a website to raise money for the search.

Rescuers deployed seven helicopters and four boats in the initial seven-day search, drafting in police, military and local people. The family then urged the British Government to put pressure on the Indonesians to keep looking, resulting in yesterday's meeting. Mrs Hoyland said: "We hope we will have a good chance of finding something that will help us to understand what happened to him."