The pair, who appeared on the National Theatre stage together, taking it in turns to play Frankenstein and his monster in Danny Boyle's stage production, had been nominated to go head-to-head for the gong at the ceremony at the Savoy Hotel hosted by Dame Edna Everage, aka Barry Humphries.
Lee Miller revealed at the pre-drinks reception he had tried "not to think about" rivalling Cumberbatch for the award.
He added: "It's just really nice for us both to be included in this evening and to be asked. It would be feel very strange to be here without him. And I'm pretty sure he would feel the same."
Gavin and Stacey star Sheridan Smith was named Best Actress for her role in Terrence Rattigan's Flare Path.
She said: "I'm gobsmacked to be honest. It's a massive honour. I'm nervous. It's just nice to be in a room with all these incredible theatre people and I'm very honoured to be here."
Kristin Scott Thomas lost out on the Best Actress award to Smith, but was honoured with the Lebedev Special Award, presented by Stephen Fry
She said of the awards: "Everybody seems to love theatre and London seems to function really well for theatre, and it's just the right place to be. For me anyway."
Miranda Hart presented The Ned Sherrin Award for Best Musical to comedian Tim Minchin and the rest of the team for Matilda the Musical, which has recently transferred to the West End.