Mulligan was nominated for an Oscar for her work in "An Education." She also starred in the films "Wall Street: Money Never Sleeps" and "Never Let Me Go."
Mumford leads the band Mumford & Sons.
"They're a great couple," a friend of the pair told UsMagazine.com. "Very sweet."
No details about how Mumford proposed or when the couple plan to exchange vows were immediately reported.
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