Civil registration of births, marriages and deaths in the United Kingdom is a nineteenth-century innovation, based on the previous practice of keeping parish records of baptisms, marriages, and burials. The history is different but parallel in England (and Wales) and Scotland.
What the churches were originally trying to do was to record information about their own ceremonies, because there are religious consequences to being baptized, married, etc. Civil law follows: you might have to prove in court that you were validly married to such-and-such a person, now deceased, and therefore had the right to live in his home as his widow.
The parish system, because of its general utility, was regulated by legislation. In England, it was made mandatory in all parishes in the middle of the sixteenth century (although in practice, this happened at different rates in different places). Legislation in the following centuries covered the manner of keeping records, penalties for non-compliance, and fees for registration. For example, by the late seventeenth century you would have to pay sixpence to register the birth of each child, and a massive 40 shillings if you failed to do so within five days of the event. Registration also served as a device to give nonconformists an incentive to join the established churches, as there was no secular way to prove age, and few ways to marry.
With liberalisation of religious strictures in the nineteenth century, the civil system began in England and Wales in 1837, and in Scotland in 1855. Under the Acts (6 Will 4 c.33, 17&18 Vict c.80), records were kept by governmental authority, with no religious qualification required. This was helpful for non-Anglicans or non-Presbyterians wanting to live their lives, and helpful for the government for having a more complete set of records for the population in general.
Currently, registration of births is free, but there are various penalties for not doing it in time, and it costs money to get copies of birth certificates. The fees are not based on any estimate of lifelong earning power or anything of the kind. There was a very brief period (1695 to 1706) where in order to fund a war with France, the government levied a variable rate tax on parish register entries. The rates depended on the degree of the person registered. It was abolished due to its considerable unpopularity, also resulting in low rates of compliance and therefore revenue gained.
The law, An Act for granting to his Majesty certaine rates and duties upon Marriages Births and Burials and upon Batchelors and Widowers for the terme of Five yeares for carrying on the Warr against France with Vigour, 6&7 Wm&Mary c.6, now called the "Duties on Marriages, etc. Act 1694", set out the following for births:
- Paupers: Free
- Most people: Two shillings
- Aristocrats: Between twelve and thirty pounds depending on rank, and with a surcharge for the eldest son, in addition to the two shillings.
- Baronets, knights, lawyers, academics, gentlemen and senior clergy: Between one and five pounds, plus the two shillings.
- Anyone not included in the above but who is rich: Twelve shillings.
Similar fees were charged for marriages and so on. I believe this is the only time in UK law when there were differential fees for registration depending on the status of the parents. The scale was presumably based on the idea that wealthier people could afford to pay more. There were no legal consequences for the child as a result of the different fee paid, except insofar as they would be disadvantaged later in life if they were not properly registered.
The law was repealed and the "Warr against France" has also been over for a long time.
As usual, the "sovereign citizen" conception is completely bogus. There is not, and has never been, any notion of a birth certificate being a financial instrument. The confusion may be due to the word instrument being used for lots of different kinds of official documents, as well as a general boneheadedness about how the law works. A birth certificate is a convenient way to prove the circumstances of your birth, and for the government to collect statistics. Indeed, a paper copy of a certificate is just a way to make the management simpler - you can get many copies or none, at your option - since it saves effort compared to inspecting the centralised registers themselves.