Having been on the losing side in the 17-day civil war of 1159 now known as the Heiji Rebellion (Heiji-no-ran), Minamoto Yoritomo found himself in exile in Ito Province, part of what is now Shizuoka-ken. He spent a lot of time in a shrine then known as Mishima Myōjin, now called Mishima Taisha, praying for a recovery in the fortunes of the Minamoto clan. The kami responded, no doubt aided at least in part by Yoritomo’s own machinations, and by 1180 he was able to raise an army strong enough to allow him to begin establishing a power base in Kamakura. One of the first things he did on entering Kamakura was to enshrine the deity of the Mishima Myōjin Jinja in what is now Morito Jinja through the Bunrei/Kanjō process. Hayama is very close to Kamakura.
The Azuma Kagami tells us that one Shōgun after another
Ōyamazumi-mikoto (22) 大山祇命
Kotoshiro-nushi (90) 事代主命
Oseki Inari-Sha おせき稲荷社
Earliest mention of: 1180?
Annual Festival: Sept. 7/8
came to visit the area and the shrine and participated in martial sports there such as Horseback Archery ("Yabusame" 流鏑馬) and Sumō. This Shōgunal patronage outlived the Kamakura regime, and in 1591 the first Tokugawa Shōgun, Ieyasu, awarded the shrine an annual stipend of seven koku of rice (one koku was considered sufficient to feed one man for one year). Two famous visitors the shrine history notes are those of the fifth Tokugawa Shōgun, Tsunayoshi, in 1674, and of the Empress Dowager Eishō-Kōdaigō (英照皇太后) in 1892.
Morito Jinja was also on the local Nana-sei-harai (七瀬祓, lit. "seven flowing purification") circuit. This was originally a custom of the Imperial Court which was adopted by the Kamakura Shōgunate. In its original form it involved seven people being sent out from the court on behalf of the Emperor to seven local sites associated with rivers and/or seas to offer prayers and incantations to seek recovery from or ward off calamities. Enoshima was also on this circuit.
As a glance at a map shows the shrine is situated on an estuary overlooking Sagami Bay, and this proximity to the sea lends it an interest it might not otherwise have. The photo on the left of the second rank below is of Najima Island, 700 metres away from the shrine, and on a clear day Mt. Fuji can be seen towering behind it (the shrine's home page sometimes opens to a photo of this). One of the in-ground shrines, the Chikurei Sha, is described as a shrine for pets, I have not come across such a shrine before.