Hi Dom,
John COX and Sarah WILLIS are my 3 x Great Grandparents. I have good DNA matches to other children of Henry COCK or COX and Ann ANNIN/G or HANNIN/G so am relatively happy at the moment that they are the parents of John.
There is a marriage for Henry COX to Ann HANNIN 16 Jul 1834, St Leonard Shoreditch
There is a baptism for John COX son of Henry COX & Ann on 25 Jul 1837 (born 4 Dec 1837) at St Luke, Finsbury.
I have Henry & Ann and family in the 1851 census living in Sturch Alley (?) St Luke, Finsbury with 5 children Henry, John, Ann, Betsey & Thomas. This gives Henry's birthplace as Postwick, Norfolk (I think, it is hard to read!). The name in the census looks much more like COOK so has possibly been mis-transcribed.
There is a baptism of a Henry COCK 23 Mar 1811 in Postwick, Norfolk to John & Charlotte COCK.
There is a marriage of John COCK to Charlotte REYNOLDS in Easton, Norwich, Norfolk 3 Dec 1805.
I found no specific baptism for John COCK but there is a couple (Edward COCK or COX and Jemima) having children in Postwick at the right time and there is a "gap" in the children at the right time for John. For the time being they are my hypothetical parents for John.
There is a marriage for Edward COX to Jemima KETTERINGHAM in Postwick, Norfolk 19 Apr 1756
I have not gone any further back on this COX/COCK line as yet.
A lot of my tree is a research work in progress so I would certainly suggest that you double check anything I have here for yourself to make sure you are happy that this is all correct but I hope it might give you some pointers.
I will reply separately regarding Sarah Willis and what I have in terms of her parents.