Jackson took to the stage for the first time in 25 years following her stepping down from a career in politics.
The actress won The Trewin Award for Best Shakespearean Performance and was presented the award by Susannah Clapp, critic at The Observer.
Before the ceremony, Jackson responded to playwright Ronald Harwood's comments last year that casting women in male Shakespearean roles was "astonishingly stupid". She said: "He clearly hasn't seen many productions. I think the 'gender-bender' issue has gone, at least I hope it has."
American playwright Annie Baker won Best New Play for The Flick, which ran at the National Theatre in April. Tim Minchin's new musical Groundhog Day won The Peter Hepple Award for Best Musical - new or revival, while John Tiffany took home Best Director for Harry Potter and the Cursed Child.
The award for Best Designer went to Christine Jones for Harry Potter and the Cursed Child, while Charlene James won Most Promising Playwright Award for her play Cuttin' It about FGM in Somalia, which ran at the Young Vic, Royal Court, Yard Theatre, Birmingham Rep and Sheffield Crucible.
Anthony Boyle, who plays Scorpious Malfoy in Harry Potter and the Cursed Child, won The Jack Tinker Award for Most Promising Newcomer - other than a playwright.
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