The survey from MasterCard to mark its partnership with the 2012 Olivier Awards also found that the Harry Potter series was the film the public most wanted to see on the boards.
Paul Trueman, head of marketing at MasterCard UK & Ireland, said: "London's West End is already celebrated all over the world for its spectacular productions and it's interesting to hear what other iconic films, programmes and actors the British public would like to get even closer to through the magic of theatre."
Downton Abbey reportedly polled almost twice as many votes in the TV-to-stage poll than the second-placed Sex and the City and almost three times as many as current US hit Mad Men in third.
Doctor Who stars Matt Smith and Karen Gillan won the vote for which TV stars should move to the West End, with over a third of the mentions in that category.
Harry Potter won 34% of the vote in the film section of the poll, while its female lead Emma Watson was the film star 45% of Britons want to see make the transition to the stage.
The Olivier Awards take place at the Royal Opera House on Sunday, April 15 and will be hosted by Michael Ball and Imelda Staunton.
> James Corden, Benedict Cumberbatch dominate Olivier Awards 2012
Watch the cast of Downton Abbey talk about plans for a movie and third series of the show below: