Yes, the asylum (later Warley Mental Hospital, now a housing estate!) is in South Weald parish, despite being only the other side of the road from Christ Church, Warley! I had an ancestor in the asylum and it took me ages to find his burial, but eventually I studied the parish boundary map and all became clear that this area was actually in South Weald parish, although a long way from the village centre and parish church of South Weald.
But these babies are buried in Lorne Road Cemetery, not South Weald Church yard. If I remember rightly there are separate burial records for Lorne Road cemetery. The run-of-the-mill parish records for South Weald are for the Churchyard, at South Weald Parish Church (some miles away from Junction Road and Lorne Road).
There is a Methodist Church on Warley Hill (both Junction Rd and Lorne Road turn off Warley Hill) and a Baptist Church further up, though I know the Baptist Church would not have been there in 1881, as it started in 1884 and then it was some years after that that it moved to its present building. I do not know the date of the founding of the Methodist Church, but would guess the current building is later than 1881 too.
No - the industrial school was not a workhouse. I too wondered who the children Henry (14), Harriet (7) , KAte (5), and Emily (4)Jarvis were. They were all born Shoreditch, and the Industrial School is the "Shoreditch" Industrial School, it was, I think, for children from the East End.
I cant see them linking immediately to the Jarvis family from Junction Road, who seemed to stay in Junction Road for many a year but previously came from Sussex.