The 15 Royal Navy sailors and marines held in Iran for almost two weeks are being reunited with their families.
Leading Seaman Chris Coe was shown on Iranian television
The crew, freed by Iran's President Mahmoud Ahmadinejad as a "gift" to the British people on Wednesday, touched down at Heathrow Airport at 1200 BST.
They were then flown to a Royal Marines base in Devon to see friends and relatives, and to be de-briefed.
Tony Blair welcomed their return but accused elements of the Iranian regime of supporting terrorism in Iraq.
In a press conference given outside Downing Street, the prime minister 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.
He contrasted the rejoicing at the return of the crew 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 that 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."
Defence Secretary Des Browne said the navy crew, most of whom are in their 20s, had "acted with immense courage and dignity".
The navy personnel arrived at Tehran Airport early on Thursday in a fleet of official cars after 13 days in Iranian custody.
They had travelled first class on a British Airways flight.
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
At Heathrow Airport, the group briefly lined up in front of media before boarding helicopters.
They were then flown to Royal Marines Barracks Chivenor, in Devon, where they are being reunited with their families.
In emotional scenes, the sailors and marines dressed in military uniform, embraced relatives, friends and colleagues.
A de-briefing will take place later and they will undergo health checks.
BBC correspondents say military chiefs will be keen to assess the physical and psychological impact captivity has had on the crew.
Royal Marine Adam Sperry's family watched his return to the UK on television at home in Leicester.
His aunt, Theresa Fowler, told BBC News: "We are just longing to see him and put our arms around him and give him a kiss."
And Margaret Sperry, his grandmother, said it had been an emotional and difficult time for the family.
"I don't think I would have ever gone out of the door again if anything had happened to him," she said.
Iranian television has broadcast pictures and statements from several members of the crew, including the only woman in the group, Leading Seaman Faye Turney.
Before they left Tehran, she was shown saying: "Apologies for our actions, but many thanks for having it in your hearts to let us go free."
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.
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.