re Elizabeth and John, there are a number of sources for them on Ancestry, but I can't view them as I don't have a Worldwide subscription.
i.e.
Name Elizabeth Nichols Watson
Birth Jun 1827 England
Death 1902 Franklin County, Iowa, United States of America
So, we do have the right people, but I don't currently know much about their lives in America.
As for Jane and John Davis, I suppose we shouldn't rule out the possibility that they also ended up in America (as unlikely as that is, it would explain their absence in 1911) -- I can't find any corresponding UK deaths for them between 1901 and 1911, so I doubt they died between those census years.
My current theory is that Jane's death is:
Eliza J Davis death registered Dec 1930 aged 71 Wandsworth RD Vol 1d p 611
...that John's birth and death are:
John William Davis b Dec qtr 1857 City of London RD Vol 1c p 67
(This is the best match for a Westminster birth, as stated in the 1901 census)
John W Davis death registered Mar 1932 age 75 Lambeth RD Vol 1d p 294
Another alternative for John would be the Q1 1932 Guildford death, aged 72. I think both of these are plausible options, although Lambeth is nearer Wandsworth. Oddly, Jane's first husband (George Horne) died in Guildford as well.
The Q1 1932 Lambeth death does have a corresponding probate record; no next of kin is mentioned; not surprising given that we assume Jane predeceased John, but possibly strange that Lucy isn't mentioned... assuming they were not estranged.
...and that their daughter Lucy's death is:
Lucy L Horne death registered Mar 1959 age 69 Wandsowrth RD Vol 5d p 947
Age-wise, this matches up nicely, and we know from electoral rolls that Lucy used the middle name Louise; I can't find a baptism record for her, and so it is possible she was given a middle name when she was baptized, but I have no idea. She may well just have liked it, and decided to use it later in life.
I can't find any evidence that Lucy married (I've found possible matches, but ruled them out), nor can I find her on the 1939 register.
Any thoughts are welcome. I've tried all manner of search criteria on Ancestry, but finding John and Jane in 1911 is proving a real headache, and I don't have much information to go by in terms of finding John prior to 1901.