In 16th and 17th centuries the birth of an illegitimate child was an unusual event. Such events became commoner in the 17th century, still more common in the 18th, and so common as to create little surprise from 1750 onwards.
An illegitimate child could not take legal residence in the parish of his father or mother because he was not legitimate; hence, his legal place of residence was the parish he or she was born in in the 1700s, but after an Act in 1743-4 it took it mother’s place of settlement.
The vast majority of bastard births have no record save an entry in the baptismal register.
Removal orders or settlement certificates or examinations. Examinations often indicate the woman and her illegitimate offspring; orders for the apprehension of putative fathers, etc. and above all, bonds if indemnification given by them to the parish.
Records of illegitimacy and paternity of such children can be found in Churchwarden’s accounts, constable’s accounts and overseer’s accounts. Vestry minutes often contain agreements for the care of bastards, and the lists of apprentices and lists of newcomers to the parish are useful too (in determining paternity of bastards)
Father’s names rarely appear on birth certificates of illegitimates.
SOURCE: https://www.pricegen.com/bastardy-or-illegitimacy-in-england/
Illegitimacy in England was never common, the number of such births in the past usually being under two per cent. That number increased to three per cent between 1590 and 1610. It rose to three per cent again about 1750, slowly increased to seven per cent in the 1840s (when about a third of women were pregnant at marriage), and then declined to about four per cent in the 1890s.
The payments of John Sillifant to Thomas may not have been voluntary. It was common in cases of illegitimacy that the father might be served with a maintenance order from the county Justice of the Peace to pay for the child’s maintenance. If he was unwilling to do so, he might be imprisoned under the provisions of the Bastardy Act 1733.
SOURCE: Https://www.familysearch.org/wiki/en/Illegitimacy_in_England