What was the rate of premarital conceptions in England from 1850 to 1890?
The short answer is that we don't know.
The reason we don't know is not neglect, but the nature of the evidence available for those periods.
The key to understanding why estimates for those rates are available for some periods and not for others lies in understanding the types of records available for different periods.
The primary source for demographic information from the 1500s to 1837 are the Parish Registers which record baptisms, marriages and burials.
Parish registers were introduced in England on 5 September 1538. The Lord Chancellor, Thomas Cromwell, issued an injunction requiring that churches maintain registers of baptisms, marriages and burials.
The level of detail recorded was not standard across the whole 300 years (or, frequently, even between neighbouring parishes at the same times!). Keeping the registers was the responsibility of the incumbent.
Very broadly speaking, less information seems to have been recorded in many of the early registers (but there are some wonderful exceptions!).
Illegitimate children are often explicitly identified in parish registers using terms like "base-born", "spurious", "natural", "bastard", "imputed", or "misbegotten".
In communities that were fairly static (i.e. people tended to stay in the parish in which they were born), it may also be possible to identify illegitimate children by the absence of a marriage record for the mother. However, because of the social stigma, a child might be passed off as being the child of the mother's parents. This is not always easy to spot!
Pre-marital conception can also be identified in a similar manner. Tracing back from the baptism, if the marriage of the parents occurred less than 9 months before that date, then the child had been conceived before the marriage. Provided the parents had married in the same parish in which their children were baptised (and also provided that children were baptised soon after they were born), identifying pre-marital conception should be straightforward.
The Old Poor Law
Where they survive, another source of information for illegitimacy rates are the records of the Old Poor Law. Payments made to unmarried mothers may be recorded in parish records, and 'bastardy bonds' compelling fathers to pay for the maintenance of their illegitimate children might be issued through local 'petty sessions' courts.
The New Poor Law
In the 1830s, everything changed.
First, in 1834, Parliament passed the Poor Law Amendment Act 1834. One of the key effects of that Act was to make paternity claims more difficult, and bastardy bonds harder to obtain. In practice, in most cases this meant that illegitimate children became the sole responsibility of their mothers.
This was not an accident.
Some quotes from the Report from His Majesty's Commissioners for Inquiring into the Administration and Practical Operation of the Poor Laws, that had been commissioned prior to the Act will explain:
“A woman of Swaffham was reproached by the magistrate, Mr. Young, with the burdens she had brought upon the parish, upon the occasion of her appearing before him to present the parish with her seventh bastard. She replied, ‘I am not going to be disappointed in my company with men to save the parish.’ This woman now receives 14s. a week for her seven bastards, being 2s. a head for each. Mr. Sewell informed me, that had she been a widow with seven legitimate children, she would not have received so much by 4s. or 5s. a week, according to their scale of allowance to widows. A bastard child is thus about 25 per cent more valuable to a parent than a legitimate one. The premium upon want of chastity, perjury, and extortion, is here very obvious; and Mr. Sewell informed me that it is considered a good speculation to marry a woman who can bring a fortune of one or two bastards to her husband.”
A little later the report continues:
“Several clergymen told me that four-fifths of the women are with child, and frequently near their confinement at the time of their marriage, and that this want of chastity may be attributed in a great measure to the law of bastardy, which secures to the woman either a husband or a weekly allowance for the support of the child.”
The strict terms of the 1834 Act were mitigated by subsequent Acts in 1839 and 1844 which once again made it easier for unmarried mothers to obtain bastardy bonds (or 'affiliation orders') against the reputed father.
Where the records survive (and frustratingly, many have been lost), prior to 1834 and after 1839/1844 it can be relatively straightforward to obtain figures for the number of bastardy bonds issued. However, in itself this will be of only limited use in estimating the numbers of illegitimate children. In many cases it would simply not have been possible to prove the identity of the father and award the bond. Nebertheless, bastardy bonds are a useful supplement to parish registers.
As is fairly well known, population movement in England increased during nineteenth century, driven by the industrial revolution. Broadly speaking, there was a trend for population migration from rural to urban communities. It became increasingly common for couples to marry in one parish, and have their children baptised in another. I have seen many examples in nineteenth century census records where children are shown as being born in different parts of the country from their parents. Obviously, this makes it difficult to identify instances of pre-marital conception from parish registers.
(Families might actually move several times over a period of years, resulting in children being baptised in different parishes to their siblings.)
Another complicating factor is that central-registration of births, marriages and deaths was introduced in England & Wales in 1837. However, registration did not become compulsory until 1875, so many births simply do not appear in the General Register Office (GRO) registers. It may thus be impossible in many cases to identify instances of pre-martital conception in the most commonly used records for births and marriages in the nineteenth century.
Unlike most parish registers, the GRO registers themselves are not available to the public. Quarterly indexes are available (and can now be searched online at several sites), and birth, marriage and death certificates can be provided for a fee. The charge is currently between £11.00 - £35.00 per certificate, depending on how quickly you need it (a pdf version can also now be bought for £7.00 if the actual certificate is not required).
Thus, even if it were possible to identify and match the correct individuals, with those kinds of costs, large-scale population studies involving thousands of people are likely to be impractical for groups of volunteers!
Parish Registers after 1837
Now, the introduction of central-registration did not mean that parish registers ceased to be used. Churches continued to record baptisms, marriages and burials ("hatch", "match", and "dispatch"), and their forms were standardised to match the information contained in the GRO registers. However, as mentioned above, increased population mobility means that it is often impossible to track individuals across parishes.
A further problem is that many parish registers after 1837 have not yet been digitised.
The main driver for the transcription and publication of parish registers has been the growth of interest in genealogy and family history. Since the perception is that parish registers are a 'substitute' for birth, marriage and death certificates once you trace your family back to ancestors who were born, married or died before 1837, that became the economic driver. It was parish records before 1837 that were transcribed first. Even now, by no means are all parish records before 1837 available online, and it will probably be some time before later records also become available.
This means that researchers studying the period after 1837 through the parish registers would generally have to work from microfilm copies of the registers, trying to locate the marriage associated with a particular baptism, where that marriage, if it occurred at all, is increasingly likely to have occurred in an entirely different parish!
Published studies of populations before 1837
Even studies of populations prior to 1837 can be problematic.
One published study that you mentioned is English Population History from Family Reconstitution 1580-1837, by Wrigley et. al. This study was based on a (small) sample of parish registers transcribed by volunteers. Those volunteers also extracted the linked family information as described above.
The methodology used to obtain those results is described in Steven Ruggles' review paper The limitations of English family reconstitution: English population history from family reconstitution 1580–1837. Just 26 parishes were studied, and of those, only 12 were included in their entirety (for context, there were about 11,000 parishes in England and Wales in 1821).
Ruggles' paper also discusses potential sources of error, and considers just how representative, or not, those results might actually be.
In fairness, similar criticisms could reasonably be levelled at most of the studies that have been attempted. That is not so much a failure of the studies as it is a limitation of the available data.
The important point here is that, despite the heroic efforts of those who have contributed to the published studies, we do not yet have estimates for the country as a whole that we can safely consider to be representative for any period. It is just that studies encompassing periods before the 1830s are likely to be more reliable than those for later in the nineteenth century, for the reasons discussed above.