He adds with some incredulity, "But then they'd be back the next day. As an actor who researched and has seen footage from that time in grainy black and white, and then to be in the exact same space with some of the same people re-enacting that scene, that's a feeling that transcends acting," he says, visibly moved.
"Giving Dr King's last speech on the Capitol steps from the same pulpit, it was both eerie and inspiring."
Selma has garnered two Oscar nominations - for Best Picture and Best Original Song, leaving much of Hollywood stunned that both Oyelowo and director Ava DuVernay were snubbed.
Both the film's star and its director received nominations at the Golden Globes, for Best Actor and Best Director, respectively.
During his acceptance speech for Outstanding Performance by an Actor in a Leading Role at last week's Screen Actors Guild Awards, The Theory of Everything's Eddie Redmayne acknowledged Oyelowo (he was not nominated, most likely because screener copies of the film were not available in time for SAG voters).
DuVernay, a former publicist, worked with Oyelowo on 2012 indie Middle of Nowhere, her second film, which garnered a Best Director trophy at the Sundance Film Festival that year.
Selma is DuVernay's third effort, and boasts an impressive, curiously British cast that includes Tom Wilkinson as President Lyndon B Johnson and Tim Roth as George Wallace. Rapper turned actor Common plays James Bevel, another civil rights pioneer.
Selma has been criticised by historians and biographers for its representation of Johnson as a reluctant civil rights supporter when, in fact, he embraced the concept of the Voting Right Act of 1965 and widely considered it his own greatest achievement.
DuVernay responded with a tweet that LBJ's stall on voting was "not fantasy made up for a film".
The movie's critical acclaim can be attributed largely to the outstanding performance by Oxford-born Oyelowo, whose Nigerian parents emigrated to Britain in the 60s. His mother worked for British Rail and his father for British Airways, although these days his parents run a taxi company.
"My parents thought the idea of an art being able to make a living was just ridiculous. My dad would say, 'Why do you want to go and be with all those promiscuous types?'."
Presumably, his father has had a change of heart?
"Yes. That happened when he saw me play Henry VI at the Royal Shakespeare Company. When he moved to the UK he suffered a lot of racism. He came to the stage door after the performance and said, 'I never thought I'd see the day when a black man would play the King of England. And it is my son'. "
As a child, Oyelowo's interest in acting was sparked at a youth theatre group. When he was studying for a Theatre A Level his teacher suggested he pursue acting. Subsequently, he was awarded a scholarship to London Academy of Music and Dramatic Art. He completed his three-year course in 1998 and the following year began working with the Royal Shakespeare Company.
Oyelowo also quickly started working in television and had his greatest small screen success in spy series Spooks from 2002 to 2004.
Despite a comparatively secure career, he took a leap of faith and hopped across the Atlantic in 2007, hoping to broaden his opportunities.
"I was very successful in the UK in theatre and TV but I could feel the glass ceiling emerging because it's a cottage industry compared to America. The careers I admired, be it Sidney Poitier or Daniel Day Lewis, were operating at their highest level in Hollywood."
He smiles. "And being an ambitious upstart, I thought I'd move to Los Angeles."
In 2012, he starred in both The Butler and Lincoln.
Now, with Dr Martin Luther King, it could be said he has reached the pinnacle where African-American characters are concerned.
Oyelowo says, "I am British and although he's not part of my history or culture, I was aware of Dr King. All I really knew was the speeches and that he was a civil rights leader; that was pretty much it. But then I read the script in 2007 and just had this visceral, spiritual reaction to reading about him."
He pauses. "I determined that this was going to be part of my future."
Given his background, how did Oyelowo find common ground with the African-American icon?
"Well, he was a preacher and a Christian minister and I'm Christian as well. That was my entry point to him."
It wasn't merely his religious affiliation that Oyelowo could relate to. He, too, has suffered racism, although many years later and in different parts of the world.
"I lived in the UK most of my life but I've also lived in Nigeria for seven years. I know what it's like to be a black person in Africa, Europe and now America. It's very, very different in all those three places.
"In Africa, you are not a minority and you carry yourself differently. In the UK, racism is more about the old boys' club and it's very racially nepotistic. It's more insidious."
Ironically, the fact that he was not American helped him land the coveted role of Dr King.
"I was told I was one of the actors who came in without the burden and weight of Dr King. Understandably, African-American actors went in feeling like, 'Oh my goodness. This is our great leader'. But I didn't have that. I just approached him as a man."
Oyelowo has an interesting approach to his career in the US.
"I call it the Sidney Poitier syndrome. I truly believe he achieved what he did because he came from the Caribbean so, by the time he got to the States he had no notion of why anyone should marginalise him on the basis of race. In America, you have the legacy of slavery which weighs down on people and you have a lot of racism," he says evenly.
"There's a saying that excellence is the greatest means by which to cut through racism, and I truly believe that. If you are excellent, people will run out of excuses to stop you getting where you need to get."
Who: David Oyelowo as Dr Martin Luther King
What: Selma
Where: At cinemas from Thursday
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