Last night I was watching a "Lucy Worsley Investigates" on the Black Death. To humanize the event, she followed a family (using the Court Records of the time), and specifically a woman within the family.
Before the plague, the woman was fined for an out-of-wedlock birth, and then married off not long after. During the plague, all the woman's male relatives died, as did her husband. After, she inherited all their land, and lived into her 60s, never marrying again. It was presented as kind of a "she started on bottom and ended up on top!" type of narrative.
I was left wondering how "scandalous" the woman's out-of-wedlock birth was. Obviously it's something discouraged (hence the fine), but in her community of approximately 1,200 people (pre-pandemic), would this have been something that happened multiple times a year? Once a year? Once every few years?
(I am also assuming the rate of out-of-wedlock births would be rather lower than out-of-wedlock pregnancies, and that if the mother was married between conception and birth it was considered acceptable and not fined. Is this a valid assumption?)
It's quite hard to say for 1300s as birth and marriage figures are a bit sketchy. Someone may have a figure, but I hope the below helps tangentially answer your question (or is at least otherwise interesting!)
Peter Laslett did an entire study on "Bastardy and its comparative history" and chapter 1 has a whole load of statistics - but I can't seem to get hold of it right now!
My understanding is that out of wedlock births are somewhat rare - but mainly because shotgun marriages were so common.
There is a study by Hair about "Bridal Pregnancy in Earlier Rural England Further Examined" (Population Studies Vol 24 No 1 pp59-70). It looked at approximately 1550-1700 (so a couple of centuries after your question, but with a much better data set) and found that roughly one fifth of brides in these centuries were pregnant at the point of marriage. This increased to two fifths for later centuries (ie 18th and 19th).