Prime Minister Tony Blair has insisted no deal was done to free 15 Royal Navy crew members, as they arrived in the UK after being held in Iran for 13 days.
Mr Blair said celebrations had to be tempered with mourning
They were released "without any deal, without any negotiation, without any side agreement of any nature", he said.
British officials also denied that the UK had apologised over the incident.
Iranian television quoted a senior adviser to Iran's supreme leader saying Britain sent a letter of apology. But UK diplomats said no letter existed.
The diplomats insisted the only written communication was an exchange of diplomatic notes several days earlier.
It is thought the British note included an offer to hold discussions to clarify the border line to avoid problems in future, says the BBC's Frances Harrison in Iran.
Mr Blair said new lines of communication had opened with Iran that it would be "sensible to pursue".
But he said the UK would not stand for attempts to get nuclear weapons or to support terrorism.
Speaking as the Royal Navy crew arrived back at Heathrow airport, Mr Blair said he rejoiced at their return.
But it had to be tempered with the "ugly reality" of the deaths of four British soldiers in Iraq, killed by "a terrorist act" in Basra.
The Ministry of Defence confirmed on Thursday that four soldiers had been killed in a roadside bomb blast and a fifth was seriously injured. A Kuwaiti interpreter was also killed.
Mr Blair said it was "far too early" to point to any Iranian involvement in that particular attack.
But he added: "The general picture, as I have said before, is there are elements at least of the Iranian regime that are backing, financing, arming terrorism in Iraq."
The Royal Navy crew members were on patrol boats launched from HMS Cornwall in the Gulf on 23 March when they were detained by Iran's Revolutionary Guard.
The Iranians accused the crew of straying into its waters - the British say they were in Iraqi territory.
Mr Blair was asked if the UK had promised not to stray into its waters, Mr Blair said British forces should not be in Iranian waters - but added "it is our contention that they weren't".
The crew were flown by helicopter from Heathrow
He also denied suggestions that an Iranian official held in Iraq had been released and that consular access had been granted to others.
He said Britain had managed to secure the release of its personnel "more quickly than many people anticipated", and "without any deal, without any negotiation, without any side agreement of any nature whatever".
"We made it clear at the outset we weren't going to do that and we held firm to that position throughout," he said.
He also defended the government's "dual-track strategy" during the crisis - saying they had been open to talks with Iran, but it had also been important to mobilise international support - amid criticism that it had angered Iran.
"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," he said.
A senior government source told the BBC there had been a lot of willingness from the governments in the region and Arab world to lobby Iran, and this had an impact - as did a swift UN Security Council statement.
He added that while no deal was done by the UK over Iranians being held in Iraq, it was possible that the Iraqi government might have taken some sort of initiative.
Shadow defence secretary Liam Fox told the BBC that the government was right not to have made any concessions, but he said Mr Blair still needed to answer some questions.
"The main question is what can we do differently to prevent something like this happening in the future," he said.
"There are a number of questions about how far HMS Cornwall was away from the vessel that was being boarded. About why there wasn't proper helicopter cover - why there wasn't any patrol boat cover?"
The 15 Navy personnel have been reunited with their families at the Royal Marines Barracks Chivenor in Devon.