Well, this particular line of investigation starts with one of my great-grandfathers; James George Granshaw. He was born on 21st August 1873 to George Granshaw and Maria Granshaw (nee Buck), in Bethnal Green, London (Middlesex). James' birth certificate reveals a certain confusion over the spelling of Granshaw as in three places it was written 'Grandshaw' only to be crossed out and rewritten without the 'd'.
I also found James' parents' marriage certificate (showing that they married on 17th November 1872, also in Bethnal Green). This showed George Granshaw's father as 'James Grandshaw' (note 'd' in Grandshaw).
This is where the trail gets confused/confusing. I haven't been able to find a record of George Granshaw's birth in order to be able to trace which James (i.e. d.o.b) is his father, and hence follow the line. There is one possible George Grandshaw showing in the 1871 census index with a calculated d.o.b. of about 1851. The problem with this is that the 1881 census (which shows George Granshaw, Maria, and James) suggests a birth year of about 1853. To confuse matters further, George's marriage certificate gives an age of 20 in 1872, suggesting a birth year of 1852. Although some of these disparities can be explained through the timing of the census (etc), not all can. I suppose it is possible that he didn't know how old he was and just guessed each time...
The 1861 census shows a James Granshaw married to Sophia, and with several children, one named George, but he was aged 6 at the time, suggesting a birth year of 1855! There are no other references (that I can find) of a suitable combination of names.
There are two or three possible James Granshaws as candidates for George's father, but unless I can get some documentary evidence to link one to George, then I don't see the justification of pursuing any of them.
The one remaining line of enquiry (which I will explore as soon as I can get back to the Library) is the George Grandshaw showing on the 1871 census. If he is the same George who married Maria and became James George's father, then he does not appear to be in a household with a father named James Granshaw (as no none shows in the census index). Possibly James had dies by this time. My only hope is that either his mother or siblings will tie him back to a James Granshaw on an earlier census.
Gaie - the reference you found to a Granshaw in the 17th century seems even stranger given that this does not seem to have been followed by a slow but steady increase in Granshaws over the succeeding 150 years. Perhaps he was a lone member of the family in this country who either died without children, or returned to whichever country he'd come from. What is really strange though is that if the name Granshaw did come here from another country (rather than being adopted here by animigrant family - unlikely given that it appears aparently independently 150 years apart), then where did it come from? Granshaw sounds English - if anything! If it had originated in this country though, then why aren't there more Granshaws (it's a fairly uncommon name, even now)?
The suggestion (despite any other evidence) that the Granshaws were Huguenots is supported by the number of silk weavers (including severl I've identified) of that name.