The indie folk band's debut disc has been a regular fixture in the top ten over the past four months, but had never charted higher than fourth until now.
Florence and the Machine's Lungs follows in second place after rising up four spots, while the Glee cast's first two soundtrack releases take third and fourth.
MGMT's Congratulations is the highest new entry of the week, securing fifth position. Plan B's The Defamation of Strickland Banks lands in ninth.
Meanwhile, last week's chart-topper Justin Bieber falls to sixth place with My Worlds.
The top ten albums in full (click where possible for our reviews):
1. (4) Mumford & Sons: 'Sigh No More'
2. (6) Florence and the Machine: 'Lungs'
3. (3) Glee Cast: 'Glee: The Music, Volume I'
4. (2) Glee Cast: 'Glee: The Music, Volume II'
5. (-) MGMT: 'Congratulations'
6. (1) Justin Bieber: 'My Worlds'
7. (5) Lady GaGa: 'The Fame Monster'
8. (7) Paolo Nutini: 'Sunny Side Up'
9. (-) Plan B: 'The Defamation of Strickland Banks'
10. (8) Boyzone: 'Brother'