The billionaire entrepreneur has been tweeting proposals and offering his services to the Thai government in its efforts to extract the 12 boys and their soccer coach from a partially flooded cave.
Chiang Rai Gov.Narongsak Osatanakorn said Tuesday's rescue operation began just after 10 a.m. and involves 19 divers.
A source involved in the rescue mission who saw two of the four boys walk out of the cave said that they looked exhausted but healthy.
People across Thailand cheered the rescue operation, including at the Mae Sai Prasitsart school where six of the trapped boys are students. Rescue operations have halted for the night and will restart on Tuesday.
A BCRC spokesman said: "The UK divers are part of the core team, so they will be actively involved and that will include escorting each child out through the flooded passage".
Thai authorities said the first four rescued Sunday have been kept in quarantine until the risk of infection subsides.More news: Homicide victim's family stages him playing video game at wake
Officials are constantly pumping water out of the caves, and Sunday gave the rescue crews the best chance of recovering more survivors after days of decent weather and pumping reduced flood levels.
The youngest child, Chanin Wiboonrunreung, and 25-year-old football coach Ekaphol Chantawong, are still inside.
Two of the boys possibly have a lung infection but all eight are generally "healthy and smiling", he said.
A stretcher which is believed to be carrying a boy rescued from the Tham Luang cave is moved from an ambulance in the northern province of Chiang Rai, Thailand, in this photo taken by Kyodo July 9, 2018.
"All eight are in good health, no fever. everyone is in a good mental state", Jesada Chokedamrongsuk, permanent secretary of the public health ministry, told reporters on Tuesday at Chiang Rai hospital in the clearest update on their condition so far.
Authorities have said extracting the entire team from the cave could take up to four days, but two straight days of success raised hopes that it could be done faster.More news: Diplomatic disconnect with North Korea spells trouble for Trump
The plight of the boys, aged 11-16, and their coach, has riveted Thailand and much of the world - from the heart-sinking news they were missing to the first flickering video of the huddle of anxious yet smiling boys once they were found by the pair of British divers deep in the sprawling cave.
Monday's mission involved 18 divers from Thailand and overseas.
"The divers that were assembled from many countries are proud to have conducted this operation until its success", Narongsak said.
Monday's rescue effort took about nine hours, two fewer than the day before, in a sign of growing confidence and expertise.
The plight of the boys and their coach has drawn global attention, with divers, engineers and medics among others flying in from around the world to assist.
Another and perhaps more worrying concern was that oxygen levels in the complex were falling close to risky levels.More news: U.S. Delegates Opposed an International Resolution That Supported Breastfeeding