In the end the 1911 census might help confirm it further by showing a Joseph with a father William with the right occupation in Worcester. The 1911 census however will not be released until 2012.
In the meantime does anyone still alive in your family remember whether your grandfather had any siblings?
For information on the Worcester workhouse you need to look at this website
http://users.ox.ac.uk/~peter/workhouse/Worcester/Worcester.shtmlThe Guardian's minutes - records held at Worcester record Office might just mention the names of some people employed at the workhouse, though I don't know that that will help any in placing William.
1891 census RG12 2325 folio 45
19 Bridge Street All Saints Worcestershire
Redding, Samuel Joseph 37 Worcestershire, Head Married plumber
Redding, Fanny 34 Worcestershire, Wife Married
Redding, Evelyn Sarah 12 Worcestershire, Daughter
Redding, Winifred Mary 11 Worcestershire, Daughter
Redding, George Ravenscroft 9 Worcestershire, Son
Holland, Fanny 21 Worcestershire, Cousin
Fanny Redding's maiden name was Ravenscroft. I have no idea how this Fanny Holland was connected to the Reddings and or Ravenscrofts, but unless she turns out to be your great grandmother it won't much matter. There is no evidence as yet that this Fanny is the same Fanny in 1901 who is married to a Smith.
1871 census RG10 3049 folio 24
33 York Place Tything of Whistones Worcestershire
John R Smith 23 Worcestershire, Head Married Hosier's assistant
(on later censuses the R stands for Richard)Alice Smith 20 Worcestershire, Wife Married
Alfred Holland 16 Worcestershire, Brother-in-law Tailor
Clara J Holland 10 Worcestershire, Sister-in-law
Laura Holland 8 Worcestershire, Sister-in-law
John Holland 32 Worcestershire, Visitor Head Married Grocer
Eliza A Holland 31 Worcestershire, Visitor Wife, Married
Fanny Holland 2 Worcestershire, Visitor Daughter
------- (son) Holland under 1 mth Worcestershire, Visitor son
Fanny Griffiths 17 Worcestershire, Visitor
Alice's maiden name was Holland. She and John Richard Smith went onto have two children Charles Frederick born circa 1872 and Alice Maud born circa 1883, both born Worcester.
This Fanny Holland of course might not be the same as the Fanny with the Reddings etc. (though these are the only one of this age in Worcestershire) and the Smith connection could just be coincidental since sooner or later with such a common surname every family will get some connection with a Smith.
The only Fanny Holland of the right age on the 1881 census in Worcestershire is this one. There is no evidence that this is the same family other than some of the names and ages are similar.
RG11 2919 folio 89
Poolend St, Great Malvern, Worcestershire
John Holland 44 Buckinghamshire, Head Married Gardener
Eliza Holland 43 Kings Pyon, Hereford, Wife Married (on the 1891 census she is a widow in Malvern aged 53 born Dudley Staffordshire, still born Dudley in 1901)
Fanny Holland 10 Malvern, Worcestershire, Daughter
Mary A. Holland 8 Malvern, Worcestershire, Daughter
Emila Holland 6 Malvern, Worcestershire, Daughter
Lily L. Holland 4 Malvern, Worcestershire, Daughter
Leonard Holland 2 Malvern, Worcestershire, Son
It gets worse if you go to the 1861 census with places of birth and occupations
RG9 2108 folio 94
Rose Cottage Chesnut Walk Claines Worcestershire
John Holland 21 St Nicholas, Worcestershire, Head Married Coach trimmer
Eliza A Holland 20 Claines, Worcestershire, Wife Married
Frederic Holland 1 Claines, Worcestershire, Son
John Holland 5mths Claines, Worcestershire, Son
Jane Amphlett 13 Claines, Worcestershire, House Servant
In 1858 in Evesham registration district a John Holland married an Eliza Ann Griffiths (in 1871 a Fanny Griffiths was staying with John Holland, she is with her family in 1861 in Claines - with them is James Amphlett nephew)
Next door to John Holland in 1861 is a Griffiths family but no Fanny and a further door away are
James Holland 66 Worcester City Married Retired builder
Elizabeth Holland 62 Worcester City Married
Sarah Holland 25 Worcester City Daughter
Charles 13 Worcester City Grandson
Trying to work out whether all these censuses are the same family would take Fanny's birth certificate for her mother's maiden and her marriage certificate to prove it was Fanny Holland who married William Smith and had a father called John. So really only worth untangling if there seems any evidence that it is worth doing so and you are some way off that. Otherwise untangling all these Hollands is really somebody's else's problem.
Regards
Valda