Thank you all so much! Some great ideas to follow!
I started following the close relatives address trail. I've only really researched the mother's (Mercy) family as that was my own. The children's maternal grandmother was living in Lorne St Farnworth, but not at the same address and not in that time frame so I wondered if Mercy had lived on the same street to start with when she was first married, but then her mother moved. Her mother had actually moved to Egerton St by 1871 (no. 69), while Mercy had moved there by 18th October 1875 (nr 35) and was still living there in 1881 so it makes sense that she moved there. So, 35 Egerton St must have been their family home. It seems Mercy was living at 2 Lorne St when her little girl was christened in 1873 so they must have moved from there between 3rd and 19th October when their kids were sick. Maybe they had been waiting for a house to become available closer to Mercy's mother and just took it when one came up. Bad timing, really.
So I started looking at the children's father's family. The father's eldest sister had the same name as the little girl who died (Christiana) so was easy to find. And yes, they (the father's siblings and parents) were living at the death registered address in Market St in both 1871 and 1881!
So It seems that the family home was Egerton St where the 2nd twin died (father was present at the birth). 34 Market St was the father's family's home where his parents and all siblings except one were still living. They must have taken in the little girl to avoid contaminating the 2nd twin who was already sick and losing weight. Father was present at the death so I imagine mother was with the second twin at home. Can you even imagine - taking all that trouble to make sure your other child doesn't get scarlet fever because you're already worried about him, having just lost his twin, and not seeing your 2 year old daughter much during those 2 weeks, and then she dies. Then the last twin dies anyway the next day. Makes it sound even more horrific! They must have been desperate.
I also looked up the father's occupation although they could still put an occupation down when they were out of work.
In 1871 he was a railway telegraph constructor.
When they married in November 1871 he was a telegraph constructor and could sign his name.
On daughter's baptism in 1873 he was a labourer and they were living at 2 Lorne St, Farnworth.
On the twins' baptism in 1874 he was a labourer and only a general address of Farnworth.
On all death certificates in 1875 he was a furnace man in a chemical works.
In 1876 he was a furnace man.
In 1878 a labourer
In 1881 he was a labourer in a telegraph works.
In 1882 it's hard to see but it seems to say forsman (furnace man?) and then lots of letters.
In 1891 he was a telegraph dept (something)
In 1896 he was a telegraph inspector and they had moved to Blackburn.
Not sure if a furnace man in chemical works was a step down from a telegraph constructor? But it doesn't seem like a fun job.
Then I guess it's just left to wonder why the twins really died. There was a history of twins in that family (both Mercy's siblings and mother were twins and survived to an old age). The 2nd twin was sick first and losing weight, after 1 week of that, the first twin started with teething problems and died within a week. Second twin lasted 2 more weeks but then died of malnutrition. Perhaps as Medpat said, they both had teething problems and the second twin refused to eat? Or they were teething badly but normally and were given teething remedies which could have contained god knows what which eventually killed them? But isn't 10/11 months quite late to start teething? Surely they should have had some teeth come through by then already? It's just bugging me that an 11 month old would suddenly start to starve. Especially as they seemed to be doing all they could to save those kids.