Bonham Carter and Burton both received the BFI's highest accolade, the BFI Fellowship, at a ceremony in London in recognition of their contributions to the film industry.
The British actress was delighted to be honoured at the same time as Burton, insisting, "It's good because there's no jealousy at home. It's very handy and very thoughtful for them to give us both one at the same time."
Accepting her prize from theatre director Sir Trevor Nunn, the Alice In Wonderland star thanked her parents, who were both in the audience.
She said, "I never thought I was particularly good at this. I've certainly had my bad reviews over the years, but I kept going. My dad's motto is KBO which stands for 'Keep b**gering on', so I will, dad."
Other big winners at the 56th BFI London Film Festival 2012 Awards included Marion Cotillard's drama Rust and Bone, which was named best film.