Deaths in the South Eastern Gazette ........... 2 May 1864 at Ramsgate William QUELCH age 31 and, on the same day, his only son, also William, age 3.
From the same newspaper (dated 10 May 1864) ........ on Sunday week a man named QUELCH, living in the area of Addington Place, was suddenly taken ill and died Tuesday morning. A child of his died a few days before him and another has died since, his widow soon to become a mother again.
1861 12 Hertford Place, Ramsgate
William QUELCH head mar 28 mariner b.Ash
Tamezon wife 36 b.Ramsgate
Louisa dau 8 b.Cripplegate London
Wm Fred'k son 2m b.Ramsgate
Mary Jane WEST sister unm 24 dressmaker b.Ramsgate
RG9/537 folio 123 page 4
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There is a merchant navy record (or two) indexed for a William QUELCH born Kent (1833 Ash) see
http://www.familysearch.org and Findmypast which might be useful in establishing when he was actually sailing
William QUELCH m Tamzen WEST 1860 at Christchurch, Ramsgate. Ramsgate Library may well have the registers on film or fiche and do a lookup for you otherwise it is available on Findmypast (pay per view) QUILCH. So if Louisa was actually William's child and born within 9 months of him being imprisoned 1851/1852 I suppose it could suggest that he was her father thus the absence of a few years and no marriage until 1860
"Tanzzen" WEST age 20 born Ramsgate was a general servant at 5 Castle Street, St Giles, Cripplegate 1851 census HO107/1525 folio 383 page 44.
1851 18 Longacre, St Martin in the Fields, Middlesex
Robert QUELCH head mar 40 carman b.Ashford Kent
Mary Ann wife 46 b.Ashford Kent
HO107/1482 folio 62 page 35
I'm pretty sure that the birthplaces should actually be Ash and not Ashford ........... Robert dies and she goes on to marry Thomas WALES as found 1871 census.
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There's also the trial of a William QUELCH 1848 age 15 who was acquitted for larceny which I expect you've noted in case it is connected?
Casalguidi