The Sherlock star plays computer pioneer Alan Turing in wartime drama The Imitation Game.
Speaking at the film's European premiere in a wet and windy Leicester Square, Cumberbatch described Turing as "an extraordinary man".
His performance is already being tipped as an Oscar contender.
"To be asked to play such a phenomenal human being - a true English hero - is a great honour and comes with a great responsibility," Cumberbatch said.
He added that he had known "embarrassingly little" about Turing before he made the film.
"That's the tragedy of this man's extraordinary life - his achievements and his heroism and his criminal prosecution are not well known. He should be on the front cover of text books."
Co-star Keira Knightley and other members of the cast - including Charles Dance and Mark Strong - also braved the rain on the opening night of the festival. Knightley plays Turing's close friend and fellow-code breaker, Joan Clarke.
London Film Festival director Clare Stewart described The Imitation Game as "a remarkable British film with great British talent in front of the camera".
The Imitation Game is largely set at Bletchley Park, Buckinghamshire, where Turing and his team attempted to decipher German messages to help end World War Two.
Turing killed himself in 1954, two years after being prosecuted for gross indecency after he fell foul of anti-gay laws at the time.
Turing received a posthumous royal pardon in December 2013, with Justice Minister Chris Grayling saying he undoubtedly shortened the conflict and saved thousands of lives.
Earlier on Wednesday, Cumberbatch said he understood why some people drew comparisons between Turing and his TV role as problem-solving genius, Sherlock Holmes.
"I didn't read the script and go 'this is Sherlock in tweed'," he said. "I liked how uncompromising he was and I suppose that's a strong trait in strong characters."
The film's Norwegian director, Morten Tyldum, described Turing as "an unsung hero who achieved so much... he was ahead of his time and outside of his time and was carrying all these secrets".
Sherlock Turing
Sherlock Turing
This could be good
“If you trust in yourself, and believe in your dreams, and follow your star. . . you'll still get beaten by people who spent their time working hard and learning things and weren't so lazy.”
Re: Sherlock Turing
Well, just because Cumberatch is in it doesn't mean it's going to be good...
Let's not forget this straight to cable turkey:
Let's not forget this straight to cable turkey:
