I knew it! I've photographed enough of the churches around Lancaster to recognise the architects' styles, and this is indeed another by Lancastrians Paley & Austin, using local slate rather than Lancashire sandstone. Built in 1883-4, it occupies the site of a 12th Century chapel.
I wonder if the weathervane is of significance; Torver is neither coastal nor on the lakeshore. It may just be a christian ichthus. Interestingly, it's rather similar to the one on another Paley & Austin church, St. Mark's in Dolphinholme, south of Lancaster.