Two Strangers (Carry A Cake Across New York) began as The Season in Ipswich and Northampton.
The Hollywood star says he is "thrilled" to be recognised for the play Good Night, and Good Luck.
Bette Midler and Hannah Waddingham pay tribute to the Broadway and West End star.
Jeremy Strong and Sarah Paulson are also among the winners at the event celebrating Broadway theatre.
Award winning actor Alan Cumming is aiming for a West End hit with A Strange Loop, currently at the Barbican Theatre in London.
The Tony Awards, Broadway's biggest night, saw success for several British names on Sunday.
The five-part series on national parks takes in locations including Chilean Patagonia and Indonesia.
The singer and actress becomes the 17th person to collect Emmy, Grammy, Oscar and Tony Awards.
The show about Henry VIII's wives leads a good year for UK talent in the Tony Award nominations.
