Yes, British pound sterling (GBP) is fully accepted and legal tender in Jersey. The Jersey pound (JEP) exists as a separate currency but is pegged 1:1 to GBP and issued by the States of Jersey.
Euros and US dollars are accepted in some tourist-oriented businesses (hotels, large retailers) but at unfavorable rates. Sterling (GBP or JEP) is the default.
Jersey is a Crown Dependency, not part of the UK or EU. It controls its own monetary policy but maintains the sterling peg for stability.
Bring GBP cash or cards; spend JEP change before leaving the island.