The turning point, at least among elites, began in the late 18th century. By the 19th century, the choices of the couple began to count for more and the traditional methods of arranged marriages had began dying out.

For example, Queen Victoria's mother and maternal uncle both wanted her to marry one of their Coburg nephews, but rather than outright arrange the marriage, they just invited Ernest and Albert to visit her often and hoped she would take a shine to one of them (which, as we all know she did). Victoria and Albert then used similar methods to marry off their nine children. Marriages weren't outright arranged as they had been in the 18th century and earlier, but the royal children instead were introduced to other suitable royals in hopes that they would meet someone they liked. This still isn't quite like modern dating and marriage, but it's still not traditional arranged marriage, either.

Among British nobility in the 19th century, there was also a change from more traditional arranged marriages to allowing some degree of choice with the birth of the London social season, which became the time for unmarried children of nobles and gentry to find matches. While they are fiction, Sense and Sensibility and Bridgerton both depict the London season.

It's more difficult to gauge changes among common people, but it is known that the Industrial Revolution is one main catalyst in the changing of marriage and courtship. One problem is that records of peasant marriages in the medieval and Early Modern Period are sparse, so comparing and contrasting is not as easy as it for royalty and nobility.