The 'Jurassic Park' director's upcoming second studio album 'I Shouldn't Be Telling You This' features Anna - who composed the music for the fifth season of the hit British drama 'Peaky Blinders' starring Cillian Murphy as Thomas Shelby - on a mash-up of Wes Montgomery's 'Four on Six' and Marianne Faithful's 'Broken English'.
And the 38-year-old singer/songwriter has admitted she couldn't believe it when the Hollywood legend wanted to Skype her about working with him on the duet.
Speaking exclusively to BANG Showbiz at the 2019 Hyundai Mercury Prize music awards at London's Eventim Apollo in Hammersmith on Thursday (19.09.19), Anna said: ''It was pretty insane and quite surreal.
''I did a song on his album.
''He emailed. We were going to have a Skype conversation but somehow that hasn't happened yet.
''But I am hoping we will.
''Apparently he's happy with what I've done.''
Anna received her third Mercury Prize nomination this year for her third album 'Hunter', and says the songs have ''become their own thing'' and are even ''wilder'' performed live.
She said: ''From playing it live it has got wilder than it was than when I recorded it.
''I guess the experience of singing these songs every night, they just become their own thing, the beast that can't be controlled.
Jeff's second album - which also features The Mildred Snitzer Orchestra from his debut album - is released on November 1 via Decca Records.
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