Just a short note and a tip of the hat to Dr. Josef Augusta (1964) who wrote: “Ichthyosaurs are very closely related to Mesosaurs…”
This was prior to the publications of the most primitive and mesosaur-like ichthyosaurs, like Utatsusaurus, and prior to the publication of aquatic mesosaur ancestors like Claudiosaurus and several other sisters. See the full tree here. Among modern paleontologists, almost none have tested this relationship with the exception of Maisch (2010) who still wasn’t sure. He also considered procolophonids as possible ancestors.
Augusta J and Burian Z 1964. Prehistoric Sea Monsters. Paul Hamlyn, London. 63pp.
Maisch MW 2010. Phylogeny, systematics, and origin of the Ichthyosauria – the state of the art. Palaeodiversity 3: 151-214.