Many thanks for the additional bits of information, folks.
Keyboard86, I am not sure whether the family in the 1861 census is the same family or not - the names are correct, they were living in a similar area of London, but the place of birth for both William and Amanda being born in Bury, Suffolk is a bit confusing as, to my knowledge, Amanda was born in St Pancras and died shortly after giving birth to Amy Georgiana's birth in 1870. Amanda's death was in 1871 St Saviour (Southwark), aged 26, in Southwark - same area as the 1861 census that you found but my William R wasn't actually a widower at that time.....interesting conundrum!
1851 census - I hadn't heard of Emily, but looking at births on FreeBMD I found these:
Births Mar 1851 (>99%)
Whitehair Emily Adeline Bermondsey 4 9
Births Mar 1855 (>99%)
Whitehair Emily Matilda St Pancras 1b 110
The name Emily Adeline caught my eye as my Grandmother was Adeline Agnes Haines...after her great Aunt perhaps, but on the other hand there is Emily Matilda, named after her paternal grandmother, Matilda nee Brown. I can only surmise that Emily b1851 might have died as an infant and 2nd Emily was named after her..........I need to do some more research I think!
Thanks again for everybody's input and for the details from the marriage cert., CaroleW.
I think I also need to check the ships' lists to find out exactly when William emigrated to America - a bit too late to start that now, so a job for the weekend, I think.
Sue