The Attorney General, Jeremy Wright, will make a statement to MPs about Abdel-Hakim Belhaj and his wife Fatima Boudchar, who allege the United Kingdom was involved in their unlawful rendition to Libya.
Belhadj, who was a known opponent of Gaddafi's regime, and his pregnant wife were abducted by U.S. Central Intelligence Agency agents in Thailand and then illegally transferred to Tripoli with the help of British spies. The British Government apologised to us for what we've been through.
On Thursday, the attorney general, Jeremy Wright QC, is due to make a statement to MPs about what is likely to be the terms of a legal deal.
Following the announcement, which Boudchar attended with her son in London, she thanked the British government for their apology.
Theresa May has personally apologised to a Libyan man and his wife for the "appalling treatment" they suffered as a result of their rendition, in which the United Kingdom played a part. "I accept the government's apology", Boudchar also added.
However, in 2011, documents revealed when North Atlantic Treaty Organisation aircraft destroyed the Tripoli offices of Gaddafi's intelligence chief, Moussa Koussa, implicated the United Kingdom government.
"It is clear that you were both subject to appalling treatment and that you suffered greatly, not least the affront to the dignity of Mrs Boudchar, who was pregnant at the time. The UK government shared information about you with its global partners".
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Mr Wright paid tribute to the "constructive way" the couple had approached the mediation, adding: "This has been a long-running and hugely complex piece of litigation, which has been hard for all the individuals involved".
In letter sent to then-prime minister David Cameron in 2013, Mr Belhaj said: Various media reports I have seen suggest that our motive for bringing this case is to enrich ourselves.
"This included in appropriate cases obtaining assurances as to the humane treatment of those concerned".
Who is Abdul Hakim Belhaj?Belhaj did not seek financial compensation, saying he only wanted an apology.
He became an opponent of Libyan leader Col Muammar Gaddafi and commanded the now defunct Libyan Islamic Fighting Group which staged a low-level insurgency war and attempted to assassinate Col Gaddafi three times.
There have been years of legal dispute over his compensation claim since.
Mr Belhaj is now a politician in Libya.