The celebrity pair have set off on a series of romantic breaks in Buckinghamshire and the Orkney Islands over the last week, the Mail On Sunday claims.
Sources state that the Never Let Me Go actress is "besotted" with the 'Little Lion Man' singer and has ditched her life in New York to stay at the folk rocker's Shepherd's Bush home.
Recalling the couple's first meeting, an insider told the publication: "Marcus invited Carey to watch him play a secret show in the basement of his friend Mike Harris's home in Nashville. She sat in the front row and while he was singing Marcus looked down at Carey and she blushed. It was clear they had chemistry.
"Afterwards, they went to the City House restaurant and dined with friends, but they sat together and acted like a couple. Carey's hoping they can spend more time together when Marcus flies back to America next month for a major tour with his band. He's hired a vintage train instead of a tour bus and has asked Carey to join him for the trip. It's early days but they seem to enjoy each other's company."
Mulligan split from her Wall Street co-star Shia LaBeouf in October, while Mumford's longterm relationship with singer Laura Marling also ended last year.