Pioneering 19th-century palaeontologist Mary Anning (Kate Winslet) is not credited properly for her discoveries by a patriarchal scientific community, which proudly displays her painstakingly excavated work in museum cabinets in London. She ekes out a thankless living alongside her perspicacious mother Molly (Gemma Jones) by selling fossils and curios to tourists through the family business in Lyme Regis. Fellow palaeontologist Roderick Murchison (James McArdle) arrives in town with his young wife Charlotte (Saoirse Ronan), who is in the grip of "mild melancholia". He entreats Mary to take care of Charlotte for "four weeks, perhaps five... no more than six" in the hope that the bracing sea air and walks along the coastline will improve his wife's disposition and reignite her maternal spirit.