Mohammed Ahmed Mohamed's claim is against the Foreign Office, Home Office, Ministry of Defence and the Attorney General.
He and another man, referred to as "CF", allege the British authorities consented to - or acquiesced in - their detention by the Somaliland authorities on January 14 2011.
The men say British "officers and agents... by their acts and omissions, procured, induced, encouraged or directly caused, or were otherwise complicit in" their detention, assault and mistreatment and torture while they were in Somaliland.
Mohamed launched his damages claim under a cloak of anonymity and was referred to in court papers as "MA".
But anonymity was lifted today following his disappearance.
Burka terror suspect Mohammed Ahmed Mohamed is seeking damages from the Government in a human rights legal challenge involving allegations of torture, it was revealed at the High Court today.
Mohamed, who was the subject of a Terrorism Prevention and Investigation Measure (Tpim), managed to dodge surveillance and disappear by disguising himself as a woman.
The 27-year-old was last seen fleeing a London mosque in the burka on Friday.
He is understood to have received training and fought overseas for al-Shabaab, the Somalia-based cell of the militant Islamist group al Qaida.
The Met Police's counter terrorism command, MI5 and the UK's Border Force are looking for him.
The founder of the mosque where the missing terror suspect Mohammed Ahmed Mohammed escaped, has told ITV News that Boris Johnson is wrong to suggest he had an accomplice.
Speaking on LBC radio, London's Mayor said he believed Mohammed wasn't acting alone when he escaped disguised in a burkha.
When asked about the comments, Khalid Rashad told us the Mayor needed to check his facts. Our Political Correspondent Simon Harris spoke to him.
The founder of a mosque where a terror suspect managed to escape while dressed in a burka says Boris Johnson is wrong to assume he had an accomplice. London's Mayor made the comments on LBC Radio this morning. But Kahlid Rashad told ITV News that he needed to "check his facts".
Boris Johnson has described the escape of a terror suspect in West London as "absurd". London's Mayor blamed coalition politics for watering down the control order system.
Plainly they are not working in the way we would like them to work in the sense that this guy Mohamed was able to flee in absurd circumstances and there must be questions about whether we should be tougher in the way we administer these things.
If a fellow can get into a burka and evade his invigilators in the way that Mr Mohamed has done, then we clearly need to look at how it is working.
Police are hunting a terror suspect who's been on the run for 3 days.
Mohammed Ahmed Mohammed has escaped surveillance by leaving a mosque in Acton disguised in a burkha. Here's Philippa Thomson.
Terror suspect Mohammed Ahmed Mohammed remains on the run after evading surveillance at a London mosque.Read the full story ›
Shopkeeper Sunny Kapoor has told ITV News missing terror suspect Mohammed Ahmed Mohamed bought five mobile sim cards from him in two weeks.
He said: "When you showed me the photo I recognised the person because last week he came to me and buy [sic] a couple of mobile simcards…
"...First he came one day and buy from me two sim cards and second time he came for two and third time he came for another mobile sim card. Five sim cards from me. Recently, in the last couple of weeks."
Home Secretary Theresa May has insisted a terror suspect who escaped surveillance by disguising himself in a burka does not pose "a direct threat to the public in the UK", despite mounting concern over his disappearance.
27 year old Mohammed Ahmed Mohamed entered a west London mosque on Friday in Western-style clothes but CCTV images showed him leaving with his face and body fully covered by a burka - the traditional Islamic garment for women.
He is the second person to breach a Terrorism Prevention and Investigation Measures (Tpim) notice since they were introduced to replace control orders in early 2012.
Mrs May told MPs: "The police and Security Service have confirmed that they do not believe that this man poses a direct threat to the public in the UK. The reason he was put on a Tpim in the first place was to prevent his travel to support terrorism overseas."
The Home Secretary Theresa May will make a statement on the missing terror suspect to the House of Commons at 3.30pm today, the Home Office has said.