Jo, one of my ancestor's was born in Essex. He and his wife left Essex in 1857 (settling in Canada). His cousin, or other somewhat close relative left Dunmow, Essex around the same time and settled in Utah. From what I gather, this family was apparently Mormon while still in England. (My ancestor wasn't Mormon.)
However, when helping several people in the past, we've found records of their ancestors as they were heading to Utah. I've done a quick search and so far do not find the same for your William Coult. This makes me wonder if he was a Mormon before leaving England.