Hi Dylan,
Its definitely going to be tricky finding Johns parentage as he only appears on the 1851 census as born London Middlesex. I believe he may have died in Manchester in the September Quarter 1851. See also
www.lancashirebmd.org.uk which has the death of a John Bates aged 41 in the sub district of Cheetham which is where Emma was living on the Census.
You may already know that his wife Emma remarried on 17th August, 1856 to a William Wright at St George, Camberwell. Her father was named as John Barnett a Silk Mercer. On the 1861 census she gave her place of birth as Bishopsgate.
I think this may be her baptism:
Carey Street, New Court (Independent)
Emma the daughter of John Barnett and Anna his wife of the Parish of St Botolph Bishopsgate in the County of Middlesex Born on the fifteenth of March, 1813 was baptised on the thirteenth day of June 1813.
Regards,
Mo