Did you have any idea that England has white sand beaches? The Isles of Scilly are an archipelago off the Cornish coast of in southwest England. They are fringed by sandy beaches and five of the islands are inhabited. Only a few thousand people live here permanently, but a regular ferry service (and small planes) connect to the mainland.
Your swim will follow one of the ferry lines, from Hugh Town (on St. Mary's Island) to Penzance. The ferry normally takes about three hours for the crossing and costs about £60. You'll have a bit more time than that and you won't have to worry about rough seas.
Penzance is the most westerly major town in Cornwall and is an historic port on Mount's Bay. Famous for its pirates (of the singing variety), it does have a mile-long beach and that's probably where you'll wash ashore.