In March, the UK launched a criminal investigation into claims that MI5 was complicit in the torture of Binyam Mohamed, a former Guantanamo Bay detainee, in Pakistan.
Rahman, 31, grew up in Britain but settled in Bangladesh in 2005, after marrying a woman he met while travelling there.
In an interview with the Guardian newspaper, Rahman said he and his wife were arrested in Bangladesh in December 2005, on suspicion of "terrorist offences".
Over three weeks of interrogation, he agreed to make taped confessions to offences, including being the "mastermind" behind the July 2005 suicide bombings in London, that killed 52 people.
He was then questioned by two MI5 agents and told them the confessions were false, the paper said.
Shortly after, they left the room and Rahman says he was beaten and told his wife would be raped.
He said that after his release he was often summoned for interrogations by MI5 and Bangladeshi officials over the next two years.
Lawyers for Rahman, who returned to Britain in May last year, claim to have evidence including eyewitness testimony and medical information.
The Briton embarked on legal proceedings after his wife and son arrived in the country last week.
Britain's home office has confirmed it received a letter from Rahman's lawyers, and said it would respond in due course.
A spokesman for the department said the British government "unreservedly condemns the use of torture as a matter of fundamental principle and works hard with its international partners to eradicate this abhorrent practice worldwide".
"The security and intelligence agencies do not participate in, solicit, encourage or condone the use of torture or inhumane or degrading treatment," he said.