Ministers have agree to pay more than £2m to the family of a prominent Libyan dissident abducted with the help of MI6 and secretly flown to Tripoli where he was tortured by the security police of the former dictator Muammar Gaddafi.

Having sought for years to avoid the agents of the Libyan dictator, Sami al-Saadi was forced on board a plane in Hong Kong with his wife and four young children in a joint UK-US-Libyan operation. They were then flown to Libya, where all of them were initially imprisoned. Saadi was held and tortured for years.

The Saadi family had accepted a settlement of £2.23m, the high court heard on Thursday. The government paid the sum by way of compensation and without admitting any liability.

Evidence of the UK’s role in the operation – believed to be the only case where an entire family was subjected to “extraordinary rendition” – came to light after Gaddafi’s fall in 2011.

CIA correspondence with Libyan intelligence, found in the spy chief Moussa Koussa’s office in Tripoli by Human Rights Watch, states: “We are … aware that your service had been co-operating with the British to effect [Saadi’s] removal to Tripoli … the Hong Kong government may be able to co-ordinate with you to render [Saadi] and his family into your custody.”

The operation was arranged in 2004 at the time of Tony Blair’s “deal in the desert” with Gaddafi, after which UK intelligence services helped track down and hand over his opponents.

Another Libyan victim was Abdel Hakim Belhaj, who was rendered alongside his pregnant wife. A letter from the MI6 head of counter-terrorism Sir Mark Allen to Koussa, also found in Tripoli, said: “I congratulate you on the safe arrival of [Belhaj]. This was the least we could do for you and for Libya. I know I did not pay for the air cargo [but] the intelligence [on him] was British.”

Belhaj is pursuing his legal action against the British government.

Saadi said on Thursday: “My family suffered enough when they were kidnapped and flown to Gaddafi’s Libya. They will now have the chance to complete their education in the new, free Libya. I will be able to afford the medical care I need because of the injuries I suffered in prison.”

He said: “I started this process believing that a British trial would get to the truth in my case. But today, with the government trying to push through secret courts, I feel that to proceed is not best for my family. I went through a secret trial once before, in Gaddafi’s Libya. In many ways, it was as bad as the torture. It is not an experience I care to repeat.

“Even now, the British government has never given an answer to the simple question: ‘Were you involved in the kidnap of me, my wife and my children?’ I think the payment speaks for itself.”

He said his family would donate some of the proceeds to support other Libyan torture victims.

“We look forward to the result of the police investigation and hope there will be a full and fair public inquiry into our case,” he said.

His eldest daughter, Khadija, who was rendered to Libya aged 12, said: “I wrote to [the then justice secretary] Ken Clarke when I heard about the secret courts plan, but he would not say that he would not seek to try my case in secret. I still feel this would have been unnecessary, unfair and unworthy of the UK. I hope the inquiry will be as open and as fair as the phone-hacking inquiry.”

Kat Craig, legal director of the charity Reprieve, which acts for the two families, said: “We now know that Tony Blair’s ‘deal in the desert’ was bought with ugly compromises. Perhaps the ugliest was for MI6 to deliver a whole family to one of the world’s most brutal dictators.”

Sapna Malik, of Leigh Day, the law firm representing the families, said: “The sheer terror experienced by the Saadi family when they were bundled on to their rendition flight and delivered up to their nemesis clearly lives with them all to this day. Having concluded one part of their quest for justice, they now look to the British criminal courts to hold those responsible for their ordeal to account and await the judge-led inquiry they have been promised.”

Belhaj, who last year led the battle for Tripoli, said: “When my friend Sami al-Saadi was freed from Abu Salim prison on 23 August 2011, he weighed seven stone. He was close to death. It is a miracle he survived his ordeal and is home with his family.”