The following web page on "History of the Mersey Ferries" is new to me --

I am also very curious about the claim made that Birkenhead Priory, which operated the ferry from Woodside in medieval times, was originally known as "Moreton Priory." This claim is rather startling. In fact, I wonder if it is true. The Victoria County History on its page on Birkenhead Priory makes no such claim.

Best regards