Whitehorn

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There is a William son of daniel and Elizabeth chr Stanford in the Vale Berks 28 May 1820 but this seems a bit late for yours however it is possible as you can be bapt(chr) anytime have several adult bap on my line again the marriage would reveal his father's name
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Looking at William and Ellen's children it looks like a m about 1849 (oldest child from census a william m Dec qtr 1844 Lambeth 4 265
Free BMD doesn't show the bride you could order that certificate-you can doit on line giving the No I've put above and specify bride Ellen if it's wrong you'll get most of your £7 back
There is also a William m in Faringdon district Sep 1841 but the brides' names are given no ELLEN Farindon 6 263
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1851there is a William 1820 from Stanford in the Vale and Caroline with numerous ch He was a rail worker so I think you can dismiss him
Yours is William Sailor unmarried 1817 this time from Gosport Hamp HO107 1660 fo 237 Alverstoke It looks like a lodging house 19 residents main family of 6 AVRITT
Dont worry about the change of birth place it often happens on census depended on who filled the forms in or gave a verbal report
1841HO107/18/1
William Whitehorn Great Coxwell Berkshire 1816 sailor with Ann Whitehorne 1784(dont forget 1841 has rounded ages)They are with Richard and Elizabeth CLARKE
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Now this is odd there is a William Robert WHITEHORN chr 31 Jul 1812 Holy Tinity Gosport to Williamand Ann C073562 1779 -1812
OK I'm confused he's too old but the right name for mother and matches the 1851 census 
I think we need help from the other Chatters on this one suggest you summaries the situation and post on England General PM me if you need help to do this, to PM by the way  click on My name that gives my profile you will see send this member a personal message  Ok must go now back this evening
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!881  RG11  579 fo 52  9 Silwood St St Olave Southwark
William Greengrocer  1820 Ferrenden Berks
Ellen from Rotherhithe Surrey 1819 makes more sense All ch from Rotherhide
Emily 23
Sarah 18
William 21
Richard Avis coal boy ser

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1891 Chiswick RG12 1033 fo 140
 William now 1818 from Farringdon a widowerBerks with son William and his wife Alice and 4 ch
So we are definately looking at Farringdon Berk for his birth
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Stanford in the Vale is very close to Farringdon so we may be looking at a relation to the Willian son of Daniel
 Post on Berkshire board for a look up in Farringdon area 1811-1820 for a William baptism
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Charlotte Sarah CARTER b 15 Apr 1816 chr 8 Sep 1816 d William and Hannah St Saviour Southwark C055182 1799-1809
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Children of William and Hannah Carter St Saviour Southwark C055182 1799-1809
Elizabeth  b 1 Apr 1814 Chr 24 Ap 1814death 27 sep 1815
Charlotte Sarah b 15 apr 1816 chr 8 Sep 1816
 C055182 is the parish number on Family Search.org
The IGI on line if there isnt a number like this it is a patron entry and can be misleading these parish numbers are usually reliable as the registers have been transcribed between the dates shown
so they had a daughter who died sad

Charlotte got married at 16 if this is right but it all fits with the 1841 census first child 1832 and she b 1816
There is a William Henry Carter chr in St Saviour 14 Jun 1781 but there was a lazy clerk as none of the entries for that period show parents names there is also a Charlotte Carter chr 5 Mar 1784 could be his sister and  its a family name
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