Asif Iqbal, Ruhel Ahmed and Shafiq Rasul, friends who became known as "the Tipton three" after their English hometown, were captured in Afghanistan in 2001. They were released without charge from the US detention centre on Cuba in March 2004.
The Road to Guantanamo, one of 19 films competing at this year's Berlin International Film Festival, combines interviews with the men, news archive material and scenes re-creating their experience. Ahmed and Rasul joined Winterbottom on Tuesday, at the film's premiere.
Rasul said: "We want to show the world what's happening in Guantanamo. What we really want is everyone to be released from there; we want the place to be closed down."
The three Britons and a fourth friend went to Pakistan shortly after 11 September, 2001, to attend Iqbal's wedding.
The film depicts them travelling next to neighbouring Afghanistan, after hearing an imam's call to help people in need there. Of the then-ruling Taliban, Ahmed said: "We had no idea who they were."
They were captured by Northern Alliance troops before being taken to Guantanamo.
In a report released by their lawyers in 2004, the three Britons claimed they suffered systematic brutality and were kept in open cages in the sweltering Cuban heat, and that the treatment forced them to make false confessions.
"We had no idea who they were"
Ruhel Ahmed, speaking about the Taliban
"We had it rough, but we didn't have it as bad as others, for example the Arabs. Because we could speak English and communicate with people, I think it made it a lot easier for us."
The United States is holding about 500 people in Guantanamo on suspicion of links to al-Qaida or the Taliban, though only 10 suspects have been charged. The prison has drawn widespread criticism in Europe and elsewhere.
Winterbottom and co-director Mat Whitecross met the three about two months after their release, and Whitecross spent a month interviewing them for material for the film.
Winterbottom won the Berlin festival's top Golden Bear prize in 2003 for In This World, a story of two young Afghans' gruelling journey to England as refugees.
Winterbottom said images of the
prisoners are dehumanising
He said The Road to Guantanamo focused on the personal story of the three - to "put faces to three of the people there and then imagine that could also apply to the other 500 people who are still there."
Winterbottom told reporters: "The starting point was to tell (about) these three people, not to tell the general political situation.
"All the images you see - it's hard to know whether it's deliberate or not, they sort of dehumanise the people there -you don't have any sense of what they're like."
In concentrating on the personal approach, the filmmakers did not seek comment from US and British authorities, Winterbottom said. He brushed aside suggestions that the film could be seen as anti-American.
He said: "I don't think the film is anti-American in a general sense."
He said that it aimed to send the message that "the fact of Guantanamo's existence is shocking and terrible, and it shouldn't be there".
Winterbottom won the Golden
Bear prize in 2003
Rasul said that "nobody's ever said, to this day, that we are innocent". The two former captives also said they had expected more support from Muslims at home after their return.
"In their eyes - not all of them - but the area we live in, we were guilty. It was hard for our families."
The film is to be shown by Britain's Channel Four television in March. Winterbottom did not give details of other release plans.