Satellite data proves 15 navy personnel being held in Iran were 1.7 nautical miles inside Iraqi waters when they were seized, UK defence officials say.
Vice Admiral Charles Style said the sailors had been "ambushed" in the Gulf after searching a vessel and their detention was "unjustified and wrong".
Tony Blair said it was time to "ratchet up" pressure on Iran, with whom the UK has now suspended bilateral contacts.
Reports suggest the only woman among the group will be freed shortly.
An Iranian foreign ministry spokesman is quoted as saying Faye Turney, 26, would be released either later on Wednesday or on Thursday.
Iran has insisted the group were in its waters when they were taken last Friday.
The eight sailors and seven marines, based on HMS Cornwall, which has its home port in Plymouth, were taken at gunpoint by Iranian Revolutionary Guards after they had searched a merchant vessel.
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
Iranian foreign minister Manouchehr Mottaki told Turkey's CNN-Turk television the 15 - thought to be at the guards' base in Tehran - were in "completely good health".
Iran's embassy in London also issued a statement in response to the UK data, in which it said the sailors and marines had been 0.5 km inside Iranian waters at the time they were seized.
The statement, quoted by the official IRNA news agency, said "the governments of Iran and Britain have the ability to solve the incident through contacts and close co-operation".
At a briefing in London, the Ministry of Defence said it "unambiguously contested" Iran's claims that the Royal Navy personnel had strayed into Iranian waters.
Speaking later, Mr Blair told MPs it was time to increase pressure on Iran "in order to make sure the Iranian government understands their total isolation on this issue".
The seizure of the personnel was "unacceptable, wrong and illegal" and the UK was now in talks with all its key allies and partners, he said.
Mr Blair added: "Our thoughts are with the servicemen and the servicewoman and their families, and their safe return is our paramount concern."
The prime minister said: "These personnel were patrolling in Iraqi waters under a United Nations mandate. Their boarding and checking of the Indian merchant vessel was routine - there was no justification therefore for their detention."
Mr Blair said the personnel had been "doing their job" and the government would be talking to international partners in Nato and the UN to reach a "sensible" solution.
The UK government said the Iranians initially said the merchant vessel searched by the navy personnel had been at a point within Iraqi waters, before later providing a second, alternative position, within Iranian waters.
In a statement to the Commons, Mrs Beckett said: "We find it impossible to believe, given the seriousness of the incident, that the Iranians could have made such a mistake with the original coordinates."
She told MPs that Britain were suspending bilateral contacts with Iran until the navy personnel were released.
Shadow foreign secretary William Hague said: "The seizure of our personnel was clearly unjustified and the evidence the foreign secretary and the MoD has presented shatters the credibility of any claim they were operating in Iranian waters."
BBC security correspondent Frank Gardner said the freeze on ties between the two countries meant that until the Britons were returned there would be "no inward or outward visits to Iran" and no UK visas would be granted to Iranian officials.