Night Birds on Nantucket, by Joan Aiken, 1966

Improbability reigns supreme in this sequel to Black Hearts in Battersea. Dido Twite, lashed to a beam and lost at sea, is rescued by a Nantucket whaler, nursed on blubber soup for nine months, and awakens to find herself in the merciful grip of a Quaker sea captain obsessed with a pink whale. Dido agrees to stay on in Nantucket and help Captain Casket's timid daughter, Dutiful Penitence, adjust to life with Aunt Tribulation. But Hanoverian plotters and foul imposters are never far away, and it takes all of Dido's pluck and sauce to stop a mad scientist from firing a gun across the Atlantic and hitting St. James Cathedral. Recommended.