Hi
There is a baptism around the same time period, though not the same area, which has an Anthony White as the father.
27th February 1814 St George in the East Middlesex born 14th February
Mary Ann White parents Anthony and Ann, Anchor and Hope Alley, father's occupation mariner
A Hannah White did have two illegitimate daughters baptised in Lambeth in 1804 and 1811 (might not be the same Hannah) both at the General Lying in Hospital.
Regards
Valda