The survey by BBC History magazine named the signing of the document on June 15, 1215, as the most appropriate date for a new British Day.
Surprisingly, the Magna Carta, which curbed the power of the monarch, safeguarded the church and gave ordinary people rights under common law, beat other significant events such as Victory in Europe (VE) Day, marking the end of World War II on May 8, 1945.
That anniversary came a close second among the 5,000 people polled followed by D-Day, a decisive World War II battle on June 6, 1944, which came in third.
The survey was launched after Gordon Brown, Britain's Chancellor of the Exchequer and the man seen as most likely to succeed Tony Blair as prime minister, proposed the idea of celebrating a national day for Britain.
Dave Musgrove, editor of BBC History magazine, said: "It's fascinating, and surprising, that an event from medieval history has come out above VE Day, all the more so when you consider that it's a constitutional rather than a militaristic moment that's been chosen."
The Magna Carta, which in Latin means "Great Charter", was a document imposed on King John in 1215 by a group of rebel barons.
It required the monarch to renounce certain rights, respect certain legal procedures and accept that the will of the king could be bound by law.
At the time it was not viewed as particularly important, but it enshrined ideas of liberty, democracy and constitutionalism.
Historians, however, remarked that the charter was more of an English rather than British event because it came before the union of Britain, which groups England, Scotland, Wales and Northern Ireland.