There are also the Chancery actions, which for the period 1800 - 1840 at least have a very large number of actions from the mothers of illegitimate children. Dozens every year I would guess.
It would be wonderful if somone would undertake to do say a sample year - perhaps extending to a decade. To look at the baptisms, presentments, and chancery actions and see to what extent these are wrongly recorded in IGI.
Also do we really know when the custom of naming switched from the male to the female side?