I cannot see a marriage for Hannah's parents William and Hannah but I may have missed it (I searched 1864 - 1871) There is quite an age difference between the parents (some 15 years if the census ages in 1871 are correct) and because their eldest child, Hannah is 4 in 1871 (b abt 1867) and William had been married before perhaps they were not legally married.
Baptism in East Moulsey, which is the place given as his birthplace in 1871:
At the parish church (spelt as East Molesey)
March 15, 1818
William Robert Osborn WINCH, parents: John (farmer), Catherine living in the parish
I think this is him - we have him in 1871, living in Petersham, aged 53, shown as father of Hannah but with a wife named as Elizabeth and occupation as 'barge carter'
Going backwards, and the age, and birthplace match, possibly coal selling from a barge
1861, address "foot of the hill"
William Winch 43, coal merchant, married, b East Moulsey
Elizabeth Winch 41, wife, married, b Caversham Oxfodshire
John Winch 17, nephew, no occupation given, b Middlesex
1851, address just given as Petersham
William Winch 33, barge horse master employing 3 men, b East Molesy
Charlotte Winch 29, wife b Oxfordshire
John Winch 7, nephew, b Middlesex
There is a death for an Elizabeth WINCH, registered Richmond (which includes district of Petersham) June qr 1864, which would fit with Hannah being born to William and Hannah in 1866.
This looks like William in 1841, at Gardeners Cottage, Bute House, Petersham
William Winch 20, coal merchant - born in county
Elizabeth Winch 15, not born in county
No relationships shown in 1841 so no idea if they were married. Ages in 1841 are rounded which accounts for the apparent discrepancy.
If you are interested I can look further for William's parents. I suspect the "Charlotte' wife in 1851 is a mistake for Elizabeth but maybe it's just another mystery!
Judith