Two-time Oscar winner Swank glittered in a shimmering silver and black Donna Karan gown and Judith Leiber clutch, as Driver upped the style stakes by wearing a gorgeous Grecian-style teal dress by Marchesa.
The two actresses play best friends in Conviction, which is based on the inspirational real-life story of unemployed single mother Betty Anne Waters, who worked tirelessly for a decade to exonerate her brother Kenny after he was wrongly jailed for murder.
"Minnie is fantastic, and so wonderful. She's got a great sense of humour and is a real girl's girl," said Swank, 36.
Returning the praise, Driver, 40, added: "She's an amazing woman. I love her. She's a gorgeous actress."
Swank - who won two Academy Awards for her performances in Million Dollar Baby and Boys Don't Cry - hopes the film, which also stars Sam Rockwell as Waters' brother Kenny, will raise awareness of the flaws in the US judicial system.
"Hopefully this will shine a bright light on the flawed judicial system in the United States," she said.
"Kenny Waters spent 18 years of his life in prison for a crime he did not commit. I have a friend who was exonerated so I've learnt a lot from him."
She added: "Betty Anne is fabulous. She is my real-life hero."
Ms Waters, who also attended the premiere in London's West End, claimed her late brother would have loved the big-screen adaptation of their story. He died after a tragic accident three months after he was released from prison.
