You will arrive, probably at Heathrow Airport.
Your best and quickest way to get to Jersey would be to fly, also from Heathrow.
Takes about an hour.
Hope you are not talking about a return to Heathrow the same day.
This would be VERY
No way to get there by sea from London.
If you want to go by sea you will need to train to Southampton and get on the Jersey fastcat. But you wont want to do that do you?
Another way......... would be to contact a fellow ribnetter and prevail on him to take you to Jersey. It's a fair way, especially in a small boat....but would be fun! And would depart from, oh, anywhere along the south coast and be totally weather dependent.