Those figures strike me as a little high compared to other national data on illegitimate births for 1700-1837 (which would, roughly and from memory, start at around 2% and rise to between 5% and 10%). A more important point I'd make is that I did say "a vanishingly small number of couples lived together as husband and wife without going through a formal Anglican ceremony", not that there were a vanishingly small number of illegitimate births, which I accept wouldn't be true. There's a stark difference throughout that period (and in fact all the way through to the late C20th) between illegitimate births per se and illegitimate births to a woman who was living in an ongoing non-marital relationship with the father, ie what we'd call 'cohabiting' today.
The reason I've been looking through posts on various genealogical forums concerning marriage laws and practices is that I'm the publisher of Professor Rebecca Probert's latest book, Marriage Law for Genealogists, which she wrote because of the ubiquity of mistakes as to the law and practices in previous centuries (especially before 1754) in existing guides for family historians. Rebecca has, as it happens, done a number of large, detailed cohort studies on illegitimacy and the prevalence of cohabitation for two other books she's written (Marriage Law & Practice in the Long Eighteenth Century: A Reassessment (Cambridge University Press, 2009) and The Legal Treatment of Cohabitation, 1600-2010: From Fornicators to Family (CUP, 1012)). She's found, consistently, that such women tended to bear a single illegitimate child and then remain single thereafter. I don't have a copy of her relevant articles or these two titles to hand, but my recollection is of a study of Northamptonshire illegitimacies for the same kind of timeframe, in which the percentage of women bearing an illegitimate child to the same father (as an indication of an ongoing, sexual, non-marital relationship) was something in the order of 0.1-0.5% of illegitimate (not total) births. That's what I'd mean by "vanishingly small".
Of course, there's always the argument that some couples had illegitimate children because they weren't validly married, even though they were living in a stable, sexual relationship, for example when one was already married to somebody else, but I think these are of a different nature to couples who set up home unmarried although able to marry if they wished. I didn't make that point in the previous post, admittedly, but Rebecca's research nevertheless indicates that these couples were for the most part anxious to be seen to be married, even committing bigamy rather than be known to be "cohabiting" (not a contemporary term in this usage).
You clearly know a lot about this area, Stan, and the Dorset Bastards study sounds very interesting. It might be that Rebecca has already come across it, but I myself haven't, I don't think, read the name anywhere in her research. Do you have any link I could pass on to Rebecca, so she can take a look at the findings? I know she'd be very interested.
Liam