Hi, Robert -
Your William Hagreen definitely married Emma Marsh, as Sophia Howard married a Levitt, with whom she is living in 1871 in Swaffham Bulbeck, along with (conveniently!) her mother, whose name is Howard.
But Emma and William are nowhere to be found in 1871 or later in the UK.
There is however the following record in the 1880 US census:
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Births Jun 1869: Hagreen Charlotte Ann Newmarket 3b 515
Interestingly, there is a William Haygreen in New York in the US 1880 census - born about 1859, both parents born in England. He is lodging with farmer Benjamin Furman and family, and is also a farmer born in NY.
And in the Ellis Island records, a William Hagreen arrived in NY on the St Louis from Southampton in Feb 1910. He is a US citizen of English ethnicity, bricklayer by trade, and was returning to his home and his wife in Superior, Wisconsin. His age on arrival was 42 yrs 1 mth, pointing to a birth date of 1868.
I saw from Tricia's reply that you were also searching for Isaac, William's elder brother.
An Isaac Hagreen/Haygreen aged 40 was living in Burlington, Kane County, Illinois in 1870. I don't have a full world sub at Ancestry, so can't view the full record.
In 1880, Isaac is shown as 54, a farmer of Burlington born in England. His wife is Ellen aged 43 born in Ireland. Illinois marriages at Ancestry shows an Isaac Hagreen married Ellen Grady in Kane County after 1851. Their children in 1880 range from John aged 20 to Etta aged 13, all born in Illinois.
In the Passenger and Immigration lists on Ancestry, an Isaac Heaygreen arrived in the US, destination Illinois. In the same list, there is also an Isaac Hagrun with the same destination. I would need the global sub to see more, which I don't have! However, I can't find these two at Ellis Island - so there's a possibility of even more severe mistranscription! Nor can I find any trace of immigration by William, Ellen and their daughter Charlotte/Lotta.
Isaac and Ellen are buried in Plato Center Cemetery, Elgin Township, as is their daughter Alice.
HAYGREEN
Alice 1863 1937
Ellen 1840 1928
Isaac 1827 1908
Interestingly, there is another older Isaac, in Rochester, Monroe County, NY. He is 70 in 1880, with wife Eliza aged 64, both born in England. Children are James aged 20 and married daughter Emma Lathrop and her child. Children all born in NY. Perhaps William above also belongs to them? (Although he could equally well belong to Isaac and Ellen, or perhaps none of them!)
Isaac and Eliza are mentioned here in a Baptist church document dated 1847, so if born in England, must have emigrated before that.
http://www.rootsweb.com/~nychauta/CHURCH/FredoniaBapt/Minutes/FBCLettersPre-1850.pdfI would suggest buying a voucher from Ancestry which would let you see the original census images of the above - they will have a lot more information, especially for 1870. You'll also be able to see the immigration records in more detail.
All the above is of course circumstantial - but William and Emma in 1880 can be identified, I should think, by sending for the birth cert of Charlotte/Lotta. That is, providing it's the right Lotta!
Anyway, I hope all this helps!
Wendy
PS
Just discovered that John and Lucy Rutter (William & Isaac's sister and her husband) also appear to have emigrated before 1870 to Monroe county, New York.