I have just come back form a holiday in Jersey.
English notes and coins are accepted everywhere in Jersey.
They have their own Jersey 1 pound note, and also Jersey �5, �10 and �20 notes, plus Jersey coins such a 5p, 10p etc.
The English and Jersey money is used interchangably and if, for example, you pay for something with an English �20 note you may get change in a combination of English and Jersey money.
As Steve D says, make sure you get rid of all your Jersey notes before you come back to the UK as they may not be accepted here.
Jersey coins seem to be accepted here as nobody pays much attention to the markings on coins.
If you need any more advice about the island then feel free to ask.