Here is a good article about English Bastardy. What it lacks is any reference to the idea that a woman could legally have a bastard within wedlock, but does indicate the local parish and church court records are your best bet:
https://wiki.familysearch.org/en/Illegitimacy_in_EnglandHowever, I found a record of a similar situation:
http://www.isle-of-man.com/manxnotebook/famhist/genealgy/illegit.htm.
Includes the idea that the child reverts back to the father at age 7 by law, if the father is paying for upkeep - new to me.
Robt Brew writes his second son for his tenancy upon certificate of the Episcopal Register that Jane Moore the sd Robts wife owns the eldest son to be an illegitimate child and the person accused make penance whereby it debars the eldest son to make title of inheritance to the Premises.
This article has fascinating stuff about parishes.
Another, more scholarly one, which addresses some of the issues raised in this thread:
From: Peter Laslett, Karla Oosterveen and Richard M.Smith (eds.), Bastardy and its Comparative
History (Arnold, 1980)
"Overall, the impression is that bastardy was treated by the church courts as the logical outcome of,
and morally equivalent to, fornication. Only a detailed comparison of sources, for instance to see
whether bastards registered in the parish registers were also presented at the ecclesiastical court,
will begin to tell us what happened in practice.
There are many other difficult points of law and definition to decide in relation to
bastardy. If a couple married and it was subsequently discovered that the marriage had to be
annulled because of some bar, precontract or affinity, for example, were their offspring
illegitimate? The position seems to have been that both by canon and common law, as long as they
had a full church wedding, and it could be shown that at least one of the partners could be proved to
have been in ignorance of the obstacle to marriage, then the children were still legitimate though
the parents were not really married. (15) These were known as 'putative' marriages.
Again, if the husband had been absent from his wife for a number of years, and she
had a child in his absence, was it a bastard? According to Coke, as long as the father was alive and
in England, the child was his and legitimate (Burn, I, p. 110). Or, what was the position of a woman
impregnated by one man who then proceeded to marry another man and the child was born after the
wedding to the latter? It was apparently believed that the child was legitimate and must be accepted
as his by the man who married the pregnant woman. "
from:http://www.alanmacfarlane.com/TEXTS/BASTARDY.PDF
