The reformed jihadi, who now runs the outreach programme at Quilliam Foundation, told Express.co.uk: "They made Islam seem relevant.
"As a young Western Muslim, I was captivated."
Attempting to explain his decision to join the radical Islamist group, he said: "I was in my teens, I wanted to learn about my faith and this group intrigued me and sparked my curiosity.
"They were young, I could relate to them and they spoke a language I could understand.
"They spoke of Islam in a way that made it come alive, presenting an intellectual version that was worlds away from the abstract and distant concepts I had previously been subjected to."
The 7/7 attacks in London and the murder of fusilier Lee Rigby are among more than 20 planned terror attacks carried out by members of Al Muhajiroun in the UK.
Security expert Raffaello Pantucci, who has written a book on the subject, said the group were not just "outcasts or losers" but serious gangsters "who are good at drawing people in and giving them these very aggressive ideas".
Michael Adebowale and Michael Adebolajo, who murdered Lee Rigby in as he walked down the street in Woolwich, south-east London, in 2013, both attended events organised by Al Muhajiroun.
ADAM DEEN Adam Deen joined Al Muhajiroun as a teenager
GETTY Protests against Al Muhajiroun in London
GETTY A bus destroyed in the 2005 London bombings
At least one of the bombers who carried out the 2005 London bombings, which left 52 dead, had met with Omar Khyam, a terrorist at the heart of a fertiliser bomb plot who had connections to Al Muhajiroun.
Al-Muhajiroun, which was founded by the Syrian-born cleric Omar Bakri Muhammad in1983, operated in the UK from 1986 until it was banned in 2005.
The group relaunched several times under different names, including Islam4UK and Need4Khalafah, to circumvent the law.
Mr Deed explained it wasn't poverty that drove him or others like him to extremism, but a failure by the Muslim community to engage young believers in a tolerant, non-extremist reading of the Koran.