1851 census living with his grand-parents Richard and Ann Pugh is William Pugh 3 (Grandson of Richard Pugh, born Dolgellau) at Crogennant, Llangelynin. Also listed in the house is Evan Pugh age 24, born Dongelly.
His mother is obviously not there on that date in 1851. She married and was living under the married name Evans.
Possible births for William Pugh are Jun 1847 Dolgellau 27 157, Jun 1847 Dolgellau 27 156, Sep 1847 Dolgellau 27 144, all who would have been 3 at 1851 census. The birth certs will not add a lot extra, but might give a guide to the father, which is actually not particularly helpful.
He is listed in the 1861 census as living in Corris. William is the only Pugh they have in that household then, and is the son of Jane Evans. So Jane Pugh must have married a Edward Evans between 1851 and about 1858
Jane Evans (nee Pugh) was born around 1824 in Llanfachreth. Llanfachreth Records do in fact show a Jane Pugh born to Richard & Ann Pugh of Buchesydd, Farmer on 3 Oct 1824, which is probably her.
However a marriage of Edward Evans to Jane Pugh is not obvious. The only two possibilites are Edward EVANS Dec 1856 Llanwnog, St Gwnog Newtown 11b 417, or Dec 1856 at Llanfyllin 11b 476. I have ordered both these to confirm her father.
By 1871 census William is a "yard foreman" and a boarder in a house in Islington, London. The house he is living in appears to have no connection with Wales
By 1881 he is married to Margaret, living at 79 Bunhill Row, Finsbury, London as a confectioner employing 1 girl. They have no children. The marriage should be William Pugh at Islington 1b 362 in Mar 1875 to Margaret Hughes. It would probably give his father.
1891 I cannot find him
1901 An insurance agent living in Islington with wife Margaret (she was born Cardiganshire). They have no children
It would seem that this line dies out as I cannot find any evidence of children