The case of Libyan politician Abdul Hakim Belhaj and his wife Fatima Boudchar who allege the UK participated in their rendition to Tripoli can be heard in the English courts.
The ruling by three judges in the Court of Appeal reverses a decision by the High Court that the couple's claim against former foreign secretary Jack Straw and Sir Mark Allen, ex-head of counter-terrorism at MI6, should be struck out.
The Master of the Rolls Lord Dyson, Lord Justice Lloyd Jones and Lady Justice Sharp said that the proceedings were not barred by state immunity and the act of state doctrine.
The couple want a declaration of illegality and compensation arising out of the UK's alleged involvement in their rendition in March 2004 and their alleged mistreatment.
In 2013, Mr Belhaj offered to drop his case for £3, an apology and an admission of liability, but this was not accepted.
In a letter sent to Prime Minister David Cameron, Mr Straw, and Sir Mark, he said: "I am making an open offer to settle our litigation.
"My wife and I are willing to end our case against the UK Government and Messrs Straw and Allen in exchange for a token compensation of a British pound from each defendant, an apology and an admission of liability for what was done to us."
The case covers a period from when they were detained by Chinese authorities at Beijing airport for two days before being deported to Malaysia and held for two weeks, then flown to Thailand, ostensibly en route to London, and later taken to Libya on an aircraft said to be owned by a CIA front company.
Mr Belhaj says that, in Bangkok, they were detained by American intelligence and he was tortured while his pregnant wife was chained to a wall. When they got to Tripoli, he spent six years in jail and his wife was released shortly before giving birth.
Today, he commented through his lawyers Leigh Day: "My wife and I are gratified by the judges' decision to give us our day in court. Our part of the 'deal in the desert' - the kidnap, the secret CIA jail, the torture chamber in Tripoli - is as fresh and as painful for us as if it happened yesterday."
Lord Dyson said that the allegations, which he emphasised were only allegations as matters stood, were of particularly grave violations of international law and human rights.
"The respondents in these proceedings are either current or former officers or officials of state in the United Kingdom or government departments or agencies. Their conduct, considered in isolation, would not normally be exempt from investigation by the courts. On the contrary there is a compelling public interest in the investigation by the English courts of these allegations."
He added: "Unless the English courts were able to exercise jurisdiction in this case, these very grave allegations would go uninvestigated and the appellants would be left without any legal recourse or remedy.
"Notwithstanding evidence from the Foreign and Commonwealth Office that there is a risk that damage will be done to the foreign relations and national security interests of the United Kingdom, we do not consider that this can outweigh the need for our courts to exercise jurisdiction in this case. Here, the risk of displeasing our allies or offending other states, cannot justify our declining jurisdiction on grounds of act of state over what is a properly justiciable claim."
The judges stayed the claims pending the outcome of an appeal to the Supreme Court against their ruling.
Sapna Malik from Leigh Day said: "The Court of Appeal has rightly recognised that the gravity of the allegations raised by our clients makes it all the more compelling for the English courts to get on and deal with their case and to reject outright the attempts by Jack Straw, Mark Allen and the government defendants to shield their conduct from judicial scrutiny.
"Our clients are now a significant step closer to seeing justice done in their case."
Cori Crider, a director at Reprieve, which also represents the family, said: "The Government so fears this case going to trial that they have stalled for years by throwing up a parade of scarecrows - claiming, for example, that the United States would be angered if Mr and Mrs Belhaj had their day in Court in Britain.
"The Court was right: embarrassment is no reason to throw torture victims out of court. The Government's dubious and wasteful delay tactics in this case need to end. Enough is enough."
Andrea Coomber, director of Justice which intervened in the case together with Amnesty International, The International Commission of Jurists, and Redress, said: "The Government's case would fundamentally undercut the international rule of law and undermine the global commitment to remedies for victims of human rights violations.
"The 'they did it too' defence traditionally hasn't worked in the playground. Yet, the UK Government would - in expanding the 'act of state' doctrine and the scope of state immunity - seek to enshrine it in common law."
"We welcome the decision of the Court of Appeal. States cannot be encouraged to supplement the international law of state immunity with their own pick and mix patchwork of domestic rules on justiciability."
Amnesty International UK director Kate Allen said: "It's only right that UK officials - right to the very top if necessary - are answerable for actions that may have led to terrible mistreatment at the hands of Gaddafi's henchmen in Libya.
"The UK has been trying to place itself above the law - a shocking response to a very serious case.
"British officials have got their paw prints all over this case and it's far too late for them to pretend otherwise.
"The UK should now stop blocking attempts to discover the full truth about the involvement of British officials in this sordid and deeply troubling affair."