Interesting approach, some improvements needed
I think it's a smart marketing approach in several ways.
1. Through viral marketing you achieve spreading the music album.
2. Instead of waiting for someone to make fun of her (as in case of amy winehouse "rehab game" ), she's the first to make fun of her with a video game; so it's unlikely that someone who comes up with a bad quality lily-allen-rehab-game will get that much media attention.
About my impressions of the game:
I played it until I was in level 10, but haven't managed to finish it. It motivated my enough to try it several times again.
The drawing were nice and fitting; except for the alcohol bottles, that looked like bad resized photographs.
The controls were ok; I found it only somewhat annoying that I could not jump onto ladders.
It seems as if there are some minor code bugs. Once a level started pitch black until I died; another time I managed somehow to fall all through that "fear wall", without getting killed. But that obviously occured very rarely.
I think it's a good idea to tune down the music, instead of completely stopping it inbetween levels.
I would like to have an option to let the music player stuck to one song. Actually I prefer the instrumental version while playing the game.
I haven't become a fan of Lily Allen music, but at least you got me to look up her Wikipedia article, because of this game ;-)