Until Christchurch became its own parish in 1865 it was known as Brimstone Hill. The origins of the name are unclear with a few possible causes.
It is said that before the land was drained, when the Fens were flooded regularly each year, there was one spot, somewhere near the Dun Cow Inn, which always stood up high above the water, and that was called the Hill. 
On Scott and Oldroyd’s farm, “The Limes”, is a piece of land which used to be called Brick Kiln Field, because at one time bricks used to be made there by hand. One of the substances used in baking bricks is brimstone. 
Another theory about the origin of Brimstone, is that brimstone was, according to the legend, the fuel for Hell Fire: not far from the village is Bedlam Bridge and one definition of ‘bedlam’, is a score of wild uproar and confusion. 
Until the turn of the century, the village name was still spelt “Christ Church”, and prior to that was known as Brimstone Hill, presumably after the butterfly (Gonepteryx rhamni known as the Common Brimstone) which used to be common in the area. 
Local oral traditional also indicates that the name of Brimstone Hill was derived from the smell of rotting vegetation during the land reclamation projects of the 19th century.
I have been told that another legend for the name’s origin stems from witches being hanged in that part of the village.
Excerpt from A Study of a Fenland Village:
The earliest evidence I can find of the existence of a settlement called Brimstone Hill, is W. Watson’s Map of the Isle of Ely, 1827 (Plate 1) on which Brimstone Hill is marked. Also, C. and J. Greenwood mark it on their map of Cambridgeshire, 1832. But Brimstone Hill was insignificant at this time, since Kelly’s Directory of Cambridgeshire, Norfolk and Suffolk, 1858 only refers to it on the map; it is not mentioned in the Directory. Brimstone Hill is recorded in the 1861 Census as part of the parish of Upwell. In fact it was not until 1862, that the village became a separate parish. Until this time it was in the parish of Upwell, with Welney and Nordolph.
Before the hamlet (as then) was named Brimstone Hill, it was referred to as Fen Drove 
- Study of a Fenland Village
- Anecdotal – source needed.