Coote was born in Frodsham, Cheshire, the daughter of the painter Mark Coote. She was educated at the Guildhall School of Music and Drama in London (though she did not complete her course), the Royal Northern College of Music in Manchester (where she came into contact with Janet Baker and Brigitte Fassbaender) and the National Opera Studio during 1995/96. Coote was a BBC Radio 3 New Generation Artist from 2001 until 2003. She sings both operatic (particularly trouser roles) and recital repertoire, in the latter often with pianist Julius Drake.