Do you know these songs?!!

Hi everyone,
I'm trying to remember two songs I heard over the summer in Forever21.
The first song has a lyric that is something like "this is my body...this is my skin...this is my brain. The singer's voice sounds like Kate Nash but I don't think it's her. She has a U.K. accent definitely.

The second song I heard in the spring(I think), and maybe several different songs faded into each other, but the part I'm trying to find is also sung by a woman with a pretty and wistful voice, and the lyric I remember is something like "you put a piece of you..into someone else's heart...

Hope you can help me..I really like both of the songs, and my searches have been in vain.
Thanks!!

The first song IS Kate Nash- Mouthwash