It is a song called 'Deep Blue Sea' by Grizzly Bear, and the version you are looking for is the Daniel Rossen Home Recording. It is on iTunes.
Sigur Rós - Brennisteinn
Ellie Goulding - Lights
Amy Macdonald - Run
The music in the current BBC Great Expectations trailer is an instrumental piece called "Outro" by M83.
Daniel Pemberton
school
I think it is the instrumtal part of "breathe me" by SIA but i cannot be certain
''Paradise'' The Ronettes.
Deep Blue Sea - Grizzly Bear
artist: Mumford & Sons track: The Cave album: Sigh No More, 2009 http://www.youtube.com/watch?v=Ay1z1Z0p6Xg
Friendly fires - Jump in the pool
Is it Fever Ray? It is very lovely.