I believe the Inn was a forner stone cottage converted to a Pub
and gets its name from the Crimena War (1854-56) and demolished in the 1890s.
I am unsure about a monastry in the area. The founder of St. Hilary, St.Germanus de Gaul, came over and establised a wooden church in 429 AD. It was not until the 12th Century that the church was built of stone. The church was modified and enlarged many times - the tower was built in 1530. Burnt down in 1857 and rebult as we see it today. With such an impressive building I doubt there was a monastry - especially as there was one in Birkenhead.