Thanks again, everyone, for the all the replies. It's made for fascinating reading and given me lots of food for thought!
Forgive me if I don't reply to every point raised.
Spring Street appears to be located in Brighton. So, Brighton was in Brighthelmstone Civil Parish? Sorry, I’m not familiar with this part of Sussex. It looks like they still were in Brighton in 1851.
There goes my moving away theory.

The civil parish was associated with the Church of St Nicholas (Brighton), and "Brighton" and "Brighthelmstone" are essentially different names for the same place, Brighthelmstone being the older of the two.
At some point between 1841 and '51, the family did move but only within the parish.
As an aside Time Runner, have you seen the reports into the suicide of Capt John EDWARDS in Brighton 1850?
I haven't, no! How exciting! Which archive did you find that in, and how did you access it? (I'm new to this genealogy malarkey and am still finding my feet).
Yesterday I found an article that stated: "the religious census of 1851 revealed that half the population did not attend any church on the census Sunday, while of those who did, only about half attended the established Church."* So perhaps the later children weren't baptized because of a change of faith or simple lack of interest. The article opened my eyes to the fact that much of the working class greatly distrusted the established church at that time. I had an idea of devout Victorians slavishly attending church on Sundays – an idea which turns out to have been utterly wrong!
*Stewart J Brown, "The national churches and the Union in nineteenth-century Britain and Ireland," in Bonds of Union: Practices and Representations of Political Union in the United Kingdom (18th-20th centuries), eds. Isabelle Bour and Antoine Mioche (Tours: Presses universitaires François-Rabelais, 2005), 57-78, online paragraph 22, https://doi.org/10.4000/books.pufr.4041 (accessed 8 November 2022).