@Lustig Andrei,
It's believed to be derived from Cockney rhyming slang and first used around the 1930's.
Grass is shortened from grasshopper, which links with copper (police), or shopper, one who "shops" information to the police.
The term Supergrass, as far as I am aware, came into frequent usage during the late 1960's, early 70's, when informants were used to break major crime organisations (The Kray Twins, etc), or terrorist networks within the IRA.
A "Supergrass" would usually be someone from within, who would be a witness on behalf of the police in return for a lenient sentence and/or new identity.
Other terms are squealer, mole, snitch, stool pigeon etc, but grass is by far the most common term that is used nowadays, certainly in the London area.
I remember walking past a really nice little sports car (MG) in the early 70's, which had all four tyres slashed, the soft top cut in several places, and the word "grass" scratched into every metal panel around the entire car.
I don't think someone was very popular.....