The reason the British soldiers would arrest Alan Breck Stewart involves two stories, that of English royal succession statrting with Charles I of the House of Stuart who was beheaded in the Civil War that led to the short Republican reign of Cromwell and that of the conflict over Protestant and Catholic primacy in England. After Cromwell, a Protestant, died in 1658, Charles II of the House of Stuart, a Protestant, was called back to England from exile in France (exile due to Civil War) and restored to the throne. He died in 1685 without producing an heir, so the throne passed in order of succession to his brother James who reigned in Scotland as their second King James and in England as their seventh King James, hence his title of King James II and VII.
This James, being Catholic in a Protestant country, wanted to attain religious indulgence for all Catholics. He went about this by imposing the Declaration of Indulgence and requiring anyone serving in the King's council, Parliament or other government posts to swear to accepting religious indulgence through the agency of three pointed questions. The Parliament didn't approve of this and arranged an overthrow by asking James' Protestant daughter Mary and her Protestant husband William of Orange to bring an army and attack James. James escaped and fled into exile in France.
We're almost at Alan Breck Stewart. When James II and VII died in 1701 while still in exile in France, King Louis XIV declared James' son James III and VIII (third and eighth) King of England. James in Latin is Jacobus. Thus the two attempts made by James III and VIII to gain the English throne from a starting position in Scotland are referred to as Jacobite uprisings. The second Jacobite uprising of James of the House of Stuart was 1745. Kidnapped is set in 1751. Alan Breck Stewart (who is descended of kings, Stuart kings) and his Scottish Highland chiefs fought with James III and VIII to attack England and take the throne from Charles I of the Germanic House of Hanover to whom the crown of England had passed. The uprisings failed, thus making all who fought for James III and VIII, including Alan Breck Stewart, guilty of treason. Hence, Alan had a price on his head and was on the most-wanted list of the British soldiers. And there you have it.