A second member of the Royal Navy crew captured in the Gulf has apologised for "trespassing" in Iranian waters, in a broadcast on Iranian television.
The crewman says he has been well treated by the Iranians.
The crewman, who introduces himself as Nathan Thomas Summers, says: "I would like to apologise for entering your waters without permission."
Tony Blair said "parading" crew in this way would only "enhance people's sense of disgust with Iran".
The UK denies Iranian claims the crew had been in its waters last Friday.
At a meeting in Germany on Friday, European Union foreign ministers called for "the immediate and unconditional release" of the sailors and expressed "unconditional support" for Britain's position.
Nathan Summers is seen alongside two colleagues, including Leading Seaman Faye Turney, 26, from Shropshire, who was shown apologising to Iran earlier in the week.
A third letter allegedly from LS Turney was released on Friday in which she said she had been "sacrificed" to the policies of the UK and US governments.
It also demanded an end to "oppressive behaviour towards other people", including prisoners at Abu Ghraib jail in Iraq.
Meanwhile, the BBC has been able to confirm the names of six of the 15 captured sailors.
Along with LS Turney and seaman Summers, who is from Cornwall, they are Paul Barton from Southport, Danny Masterton from Ayrshire, Joe Tindell from south London and Adam Sperry from Leicester.
The UK prime minister said the only possible outcome to the situation was the release of the crew.
Britain was pursuing the problem with "firmness and determination" but also with patience, he said.
Mr Blair said: "I really don't know why the Iranian regime keep doing this. All it does is enhance people's sense of disgust at captured personnel being paraded and manipulated in this way.
"It doesn't fool anyone. And what the Iranians have to realise is if they continue in this way they will face increasing isolation."
UK Foreign Secretary Margaret Beckett described the latest footage as "quite appalling" and "blatant propaganda".
She also disclosed there was nothing in a formal letter from the Iranians to the UK that suggested they were looking for a solution to "this difficult situation".
The note condemned the navy's "illegal act" and demanded guarantees against "the recurrence of such acts" in the future.
Earlier, Iranian President Mahmoud Ahmadinejad was quoted as telling Turkish Prime Minister Recep Tayyip Erdogan that Britain must apologise.
"In recent years British forces have violated international law and crossed the Iranian border," he said.
Meanwhile Whitehall sources told the BBC that procedures for patrolling in the Gulf close to the Iran-Iraq maritime border - and the equipping of British forces there - were both under review.
In the latest video, the crewman says he has been in the navy for two years, "operating mechanical warfare".
He then says: "Since we've been arrested in Iran our treatment has been very friendly.
UK VERSION OF EVENTS
1 Crew boards merchant ship 1.7NM inside Iraqi waters
2 HMS Cornwall was south-east of this, and inside Iraqi waters
3 Iran tells UK that merchant ship was at a different point, still within Iraqi waters
4 After UK points this out, Iran provides alternative position, now within Iranian waters
"We have not been harmed at all. They've looked after us really well.
"The food they've been serving us is good and I am grateful that no harm has come to us.
"I would just like to apologise for entering your waters without permission. And that happened back in 2004, and the government promised that it wouldn't happen again.
IRANIAN VERSION OF EVENTS
1 Royal Navy crew stray 0.5km inside Iranian waters
2 Iran gives set of co-ordinates to back up their claims
3 According to seized GPS equipment, the Royal Navy crew had previously entered Iranian waters at several other points
4 Iran informs Britain of the position where the crew were seized, inside Iranian waters
"Again I deeply apologise for entering your waters."
Earlier, the UN Security Council agreed a statement voicing "grave concern" at Iran's actions.
The statement also calls on Tehran to allow the UK consular access to the personnel and urges an "early resolution", including release of the crew, but stops short of "deploring" Iran's action, as requested by the UK.
Iran's UN mission said Britain's attempt to involve other nations in the crisis was "not helpful".
The Britons, based on HMS Cornwall, were seized a week ago by Iranian Revolutionary Guards as they returned from searching a vessel in the northern Gulf.