It’s called a helm roof (or a broach spire) and this design is very Saxo-Norman in origin. But the truth is that it is a relatively recent addition to both churches. St Mary’s rebuilt the tower in this way in 1856, and St Ann’s broke ground on their first ever bell-tower in 1982.
Prior to 1856 Flixton’s tower was crenelated (ie. The parapet was indented, similar to battlements.) Here’s a drawing made in 1818 by one Isaac Johnson. Is it the imagination or can stone lines be seen either side of the tower window? Is this evidence of an earlier helm roof?
I was lucky enough to visit St Mary’s, Flixton in May 2014 and wonder for myself what had existed before the Victorian tower was built.