The music in the current BBC Great Expectations trailer is an instrumental piece called "Outro" by M83.
Nancy Sinatra "Bang Bang" Cher originally recorded the song, but the version by Nancy Sinatra has received lots of airplay recently. The BBC trailer uses the remix by Audio Bootys, according to Shazam.
Sigur Rós - Brennisteinn
''Paradise'' The Ronettes.
Friendly fires - Jump in the pool
Ellie Goulding - Lights
Is it Fever Ray? It is very lovely.
Erik Satie - Gnossienne No.1
It's (CAT 00897-AA1) from Analogue Bubblebath 3 (1993) by AFX ( Aphex Twin)
It's 'Sing Sing Sing' by the BBC Band Orchestra
regards, w.
Its called Days Are Forgotten by Kasabian