British citizens do not need a passport to enter any of the Channel Islands but, as Jack indicates, the carrier MAY require proof of ID. (All airlines require some form of ID but the rules vary widely between different companies. Some will only accept passports, while others will accept passports or photocard driving licences, and yet others will accept things like bus passes as well. Most ferry companies don't insist on any form of ID, but some might do so).
Check the relevant carrier's website, or ask again here (stating how you'll be travelling) if you require further information.
It's also worth noting that the reciprocal health agreement between the UK and the Channel Islands has now been withdrawn. Health insurance is essential.
Chris