Having travelled between JER and LGW more times than I care to remember, and having spent many a year sat behind check-in desks/boarding passengers at JER, I can 100% confirm you do not need a passport to travel to JER.

Mine sits at home every time (unless I'm planning on needing it to go somewhere). You don't even need photo-ID for BA, a credit card will do.

First post by the way, long time lurker!