Barcock, Hartwell, Fuller

I have been researching my husbands family G G grand father and mother came from Cople. It is a long story but they were living under the name of Fuller, but Married in Cople Sarah Hartwell and William Barcock. Their children were baptised in London in the Barcock name but the census was reflecting the Fuller name, they lived under the Fuller name for several decades in Rotherhithe From 1861

My Dilemma is William born in 1831 and married in 1854 named his Father as William also I have looked at so many Barcocks but can not find one that would fit the bill. 

Sarah Hartwell of course is so much easier to find with her parents James and Mary Hill. 

Jenny Fuller