Investigating officers have now applied to the courts for the release of secret Government documents to help in their inquiries, a senior judge heard.
Saudi-born Mr Aamer is accusing British intelligence officers of being present and doing nothing to help him when he suffered torture in US custody at Bagram airport in Afghanistan.
Mr Aamer, 42, is also a central witness in the allegations being made by Binyam Mohamed that British agents knew of his ill-treatment while held by the US, said a QC.
A permanent UK resident, Mr Aamer is married to a British national who lives with their four children in London.
He has been detained by the US authorities as a terror suspect for more than seven years, but never charged with any offence.
His lawyers hope the Metropolitan Police criminal investigation will speed his release from Guantanamo so he can give evidence to the police in person.
Today his QC Richard Hermer described how Met officers went to the London offices of his solicitors, Birnberg Peirce & Partners, on Wednesday this week.
Mr Hermer said: "It became apparent they are now investigating allegations raised by Mr Aamer into the alleged complicity of the UK security service in his mistreatment."
The QC said it was also made clear that Mr Aamer was now a central witness in the police investigation into Binyam Mohamed's torture allegations, which also involve accusations of complicity by British agents.
Mr Hermer told Mr Justice Sullivan, sitting in London: "Events are moving at a pace that could not have been anticipated even two weeks ago."
The police had made an application to the court "for release of relevant documents". These are believed to contain evidence that confessions Mr Aamer made were obtained through torture.
The Guantanamo detainee review task force set up by President Barack Obama is shortly to decide whether Mr Aamer should at last be released from the US-run detention centre in Cuba.
The UK Government has already sent the secret documents the police now want to see to the task force review panel.
Initially, the Government refused to allow the US authorities to show them to Mr Aamer's security-cleared legal team.
But, following a High Court decision in favour of Mr Aamer, Foreign Secretary David Miliband recently agreed to hand over the papers.
The case was still officially ongoing, but today Mr Justice Sullivan decided that it should be brought to an end in view of the new police investigations.
Criticising the Government initial refusal to release the documents to Mr Aamer's American lawyers, thus triggering months of legal action, the judge said: "These whole proceedings have been a gigantic waste of time and money and that is the fact of the matter."
The judge awarded Mr Aamer's lawyers their legal costs against the Government, and ordered an interim payment of £25,000.
At previous hearings the judge was told that Mr Aamer had been detained at Guantanamo since February 2002.
Mr Hermer said he had previously been held at Bagram airport in Afghanistan after being captured by Afghan villagers in December 2001 and subjected to torture during interrogation.
On one occasion his head was repeatedly "banged so hard against a wall that it bounced" while an MI5 officer was present.
He had also been threatened with death during another interrogation at which a British agent was present, he said.
After today's hearing, Mr Aamer's UK solicitor, Gareth Peirce, said of the Met investigation: "It is potentially one of the most important criminal investigations there has been in this country.
"It is into the alleged complicity of the British secret intelligence service in torture, a grave crime against humanity.
"Mr Aamer is a victim and key witness in that investigation - and yet where is he?
"He is in Guantanamo where the police can't go to interview him. A missing witness.
"It is of central importance and urgency that everything is done to have him returned to this country."
Ms Peirce said the Government had continually asserted that it was making strenuous efforts to have him returned.
But she said: "There is no diplomatic pressure being exerted. There is none.
"The Americans are saying: 'What pressure?"'
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