Hairy,
You don't need SB clearance to arrive in Jersey, but you do to leave UK for Jersey.
If I remember you can fly via Southampton on the day, no problem (during SB hours), but if you wish to fly direct from your local airfield you must have approval from your local Chief Constable. Write to him as soon as possible, for a better chance of approval.
Do a search on the subject, a few months ago there was a thread with all this info on it.
FB