Civic engineer Mike Clayton is from Shropshire and Gary Mitchell lives in Machynlleth.
"We are humbled to have been able to provide our expertise and experience to assist in this global operation led by the Thai government".
Rick Stanton, from Coventry, said he was using a "very unique skill set" to "give something back to the community".
The three-day rescue mission kicked off on Sunday (local time) and ended late on Tuesday.
The Tham Luang Nang Non cave complex in Thailand - where 12 boys and their soccer coach were trapped for 18 days - will become a "living museum" to showcase the harrowing ordeal that unfolded in recent weeks as the world watched.
One volunteer diver, former Thai navy SEAL Saman Kunan, died last week while placing oxygen tanks deep inside the cave.
The rescue was particularly treacherous because the boys, aged 11 to 16, had to swim through tight spaces despite having no previous diving experience.
"We were very very pleased it worked out quite so well, it worked out, the results speak for themselves". So, of course there were doubts.
The rescue gripped the world, with much praise focusing on the navy SEALs and global team of divers who helped them, toiling for days in risky conditions to get the boys out.
After landing at Heathrow on Thursday, Volanthen spoke of the relief he had felt at making contact with the boys.
"We're very glad we could get you out alive. That won't happen or we'll give them hell", Chu tweeted, adding it's "a attractive story" about human beings saving other human beings. "So there was relief, tempered with uncertainty".
Mr Stanton would not describe how his team rescued the children, describing it as "too detailed for this point in time".
"When you see Australians who are modest turn up in these most hard situations around the world and they just do what they believe is the right thing", he said.
Mr Stanton declined to answer any medical questions but said: "They were carefully handled".
A mother of one of the SEAL members who participated in this operation, Sumalee Maksri, said she was delighted that her son successfully completed his mission, adding that she previously felt anxious because he did not give any details of his assignment.
Returning with Mr Stanton were fellow divers Chris Jewell and Connor Roe, both from Somerset, Josh Bratchley from Devon, Jim Warny from Co Clare, Mike Clayton from Yorkshire and Gary Mitchell from Machynlleth in Powys.
'The diving conditions were extremely challenging, there was poor visibility and responsibility for another human being's life.
"The part we played has been made out to be a lot more noble than it actually was".