The 15 Royal Navy sailors and marines held in Iran for almost two weeks have spoken of their happiness at being back in the UK and reunited with relatives.
Crew members were reunited with their families at a military base
In a joint statement released following emotional scenes at a Royal Marines base in Devon, the crew said being home was a "dream come true".
While in Iran, several said they had been well treated by their captors.
But since coming home, a report from a relative suggests one of them may have been held in solitary confinement.
Lieutenant Colonel Andy Price, at Royal Marines Barracks Chivenor where the crew are to spend the night, confirmed some of the naval personnel may have been left in solitary confinement during their stay in Iran.
"There were times when they were left alone, but we will not go into any further detail until tomorrow," he said.
Earlier, the 14 men and one woman said the welcome home was "one that none of us will ever forget".
"By staying together as a team we kept our spirits up, drawing great comfort from the knowledge that our loved ones would be awaiting for us on our return to the UK," they added.
And in a press conference outside Downing Street, Mr Blair said he was "glad" the crew had been returned "safe and unharmed".
He said "no deal" had been done with the Iranians to secure the crew's release after 13 days in Iranian custody.
He contrasted the rejoicing at the crew's return with the "sober and ugly reality" of the deaths of four British soldiers in Iraq in what he described as a "terrorist act".
The crew were flown by helicopter to Devon
And he repeated allegations there were "elements of the Iranian regime" that were "financing, arming and supporting terrorism in Iraq".
However, he said it was "too early to say" whether the UK troops had been killed by Iranian-backed insurgents.
The prime minister said the government had pursued a "dual-track strategy" of remaining open to dialogue with Iran, while "mobilising international support and pressure".
"In my view it would be utterly naive to believe that our personnel would have been released unless both elements of the strategy had been present."
Iran, however, is insisting the UK apologised in a letter received on Tuesday, but a senior government source denies there being any apology.
The US welcomed Iran's decision to free the servicemen but said the positive move would not ease tensions over its nuclear programme.
The navy personnel travelled first class on a British Airways flight from Tehran Airport to Heathrow, where they lined up in front of media before boarding helicopters.
CAPTURED NAVY PERSONNEL
Chris Air, 25, from Altrincham in Cheshire
Mark Banks, 24, of Lowestoft, Suffolk
Paul Barton, of Southport, Merseyside
Arthur Batchelor, 20, of Plymouth
Felix Carman, 26, of Swansea
Christopher Coe, 31, of Huddersfield
Dean Harris, 24, of Carmarthen, west Wales
Danny Masterton, 26, of Muirkirk, Ayrshire
Adam Sperry, 22, of Wigston, near Leicester
Nathan Summers, of Hayle, Cornwall
Joe Tindell, 21, of south London
Faye Turney, 26, originally from Shropshire
They then flew to Royal Marines Barracks Chivenor, in Devon, where they were reunited with their families.
The sailors and marines, dressed in military uniform, embraced relatives, friends and colleagues, and spoke on mobile phones to other loved ones.
Penny Banks, who was reunited with her son, Lance Corporal Mark Banks, said: "We are delighted to have him back - it was nice to hold him again."
A de-briefing and medical examinations are expected to take place later.
Chief of Defence Staff, Air Chief Marshal Sir Jock Stirrup, said: "They did exactly as they should have done from start to finish... and we're extremely proud of them," he added.
The 15 service personnel had disembarked from HMS Cornwall in the Gulf when they were detained by Iran's Revolutionary Guard on 23 March.
The Iranians accused the crew of straying into its waters, although the British have insisted throughout that they were in Iraqi territory.
It emerged on Thursday that in a television interview recorded before their capture, Capt Chris Air said one purpose of patrols in the area was to gather intelligence on any sort of Iranian activity.
The MoD said this was "entirely appropriate" and "all part of modern operations".
Commentators are divided over whether the release represents a diplomatic triumph for the UK, or a public relations coup for the Iranian president.
A senior government source said Iran realised it had made a "clumsy mistake" and had "not done itself any favours".
The source added the UK thought the matter might be resolved peacefully but had had no idea President Ahmadinejad would announce their release on Wednesday.