I'm originally from St Helens and searching my own Barton family history.
It seems we have a common ancestor in my great grandfather Peter Barton, William's father, who as you say was a fruiterer. I have gathered information from census documents and BMD going back to 1851 and this suggests the following.
William & Charlotte Barton (née Ashcroft) had 4 children - Elizabeth (1891-1944), William, your great grandfather, born in 1893, John my grandfather (1895-1972) and Eva (1910-1944)
Your William and my Peter's parents were William & Rachel (nee Coulshed) both born around 1835. It is uncertain who William Barton senior's parents were but Rachel's parents were William Coulshed (1801-76) and Mary Appleton (1807 - ?). Williams seem to run in the family (and many others I suspect during this period of history). Beyond that date things a very hazy.. I have hints for births and spouses for Appletons and one Coulshed but no Bartons.
If you are interested, you could go to the census yourself but just in case you don't want to go I can tell you that William and Rachel had many children
Jane (b1856); William Thomas (b1858), Mary (b1863), John (b1864), Edmund (b1866), Peter (1868-1947), Elizabeth (b 1871), James (b 1876), and Mary Ann (b 1880)
I came onto this St Helens site to try to find out if there was anything about Peter Barton's fruit business. Barton's pickles business is well known to us and (probably) related via his brother Edmund. I've contacted Barton's Pickles current family to ask if this is the case but they say "no"!
It is hard to believe that two brothers, one with a fruit business and one making pickles (using vegetables) are not connected; after all it's one way to use unsold stock. My Grandfather John (known Jack) told me of that he used to go by pony and cart from St Helens to Liverpool early mornings to get to the wholesale market to buy fruit and veg.
However there is another story I am trying to get evidence of - that Peter went out to South Africa in the late 1890s. There are a couple of Peter Bartons serving in the Boer Wars but nothing I can confirm with confidence.
If there is anything you can confirm, suggest, or give a different description to, I'd love to hear..
If you are interested I have a picture of Peter taken not long before his death in 1947.