Rick Stanton and John Volanthen were the first divers to reach the group nine days after they went missing in the underground network in northern Thailand.
The pair, along with a number of other British elite divers had flown to the region to assist at the request of Thai authorities.
The British rescuers were said to be “all alright” and resting after the gruelling operation.
Writing on Twitter, former Conservative Party treasurer Lord Ashcroft suggested Mr Stanton and Mr Volanthen could be awarded the George Cross or George Medal for their bravery.
The George Cross is the highest civilian honour in the United Kingdom and Commonwealth.
Please retweet if you would support a George Cross or George Medal to the two volunteer Brit cave divers who found the missing Thai boys and participated in their difficult rescue…
— Lord Ashcroft (@LordAshcroft) July 10, 2018
Others called for the pair to be given knighthoods for their “heroic efforts”.
Businesswoman Tracey Follows tweeted: “Knighthoods for the British divers involved please. True bravery and superhero status.”
Other figures paid tribute to the rescue team, including Oscar-winning US actress Marlee Matlin.
She tweeted: “Oceans of gratitude to the British Thai cave divers and Navy SEALs who got all 12 boys and their coach out of the cave.”
Former England captain Michael Vaughan wrote on Twitter: “Proud of the England Football team .. But that’s just sport .. More proud of the 7 British divers that have helped save all those boys lives in Thailand..”
Thai cave rescue: How it’s being done
The elite divers joined the vast search after the group disappeared in the Luang Nang Non Cave, Chiang Rai province, on June 23.
Mr Stanton, a fireman from Coventry, aged in his 50s, was made an MBE at the end of 2012.
He previously said his greatest achievement was helping rescue trapped British soldiers from a cave in Mexico in 2004.
Mr Volanthen, an IT consultant in his 40s and based in Bristol, was also part of a British team with Mr Stanton which reportedly set a world record for a deep underwater cave dive in Spain in 2010.
Mr Volanthen’s mother, Jill, told the Daily Telegraph: “We are absolutely so proud, but my sympathy is with the wife and family of the diver who lost his life.
“I would like to thank everybody for all their team work to get the lads out, it is absolutely lovely.”
Thai cave rescue effort | Read more
Bill Whitehouse, vice chairman of the British Cave Rescue Council, said: “We have heard from them that they are all alright, but information is pretty sparse.
“When we heard that all the boys and the last diver was out that was a brilliant moment.”
“Right now they will be absolutely knackered and it will be a question of having something to eat and drink and then falling over.”