I'm trying to wrap my head around the fact that Charles Frederick Worth, a British man formerly employed in the fashion industry in London, is the "father of haute couture," which we commonly think of as a French innovation. It seems to me that he recognized a business opportunity in Paris, moved there, and capitalized on its reputation as a fashionable place. Did he use the skills he gained in more-industrialized London to commodify French culture?
While Worth did move from England to France, it's believed he travelled for the textile business Lewis & Allenby, which he worked for, in 1845 and simply never came back. He took a while to become a success, in part because he didn't speak French! He worked at the Maison Gagelin-Opigez et Cie, a silk merchant, branching out into selling shawls and mantels. He decided to make a gown for his model that would show off the shawls well, it was very popular. The business didn't want to branch out that far so he opened his own dressmaking shop in 1857. He definitely didn't move to Paris with that intention.
As for the French v. English fashion, they were very cyclical in their inspiration of each other. The English looked to the French for high court fashion, the French to the English for sporting wear, etc. They both looked to India, China, Austria, Italy, and the entire world for inspiration as well. Paris emerges as the fashion capitol of the world in the later half of the 19th century.
Prior to this point, dressmakers (originally termed mantua-makers) were still working individually with the client to make a unique piece. Sounds like haute couture, does it not? It's not that the idea was invented in the mid-19th century, but that dress making diverged and went two very different ways. Mass-production, thanks to the industrial advances, was rapidly growing. By the end of the century women could easily buy simple clothing out of a catalogue or walk into a store and walk out with a new outfit. Prior to this a woman would buy her fabric from one store, trimmings and supplies from another, and take them to a skilled dressmaker who would fit, cut, construct, and help with design if need be. This process couldn't compete as it was with the advance of cheap clothing availability, so it became something aimed at the wealthy and elite. Worth's, or any other haute couture designers, process was very similar to the mantua-makers of the past century. Gradually, more and more emphasis was put on the dressmaker being the designer and having a "look" rather than making whatever the clients wanted. In this way we can say that Worth is the father of Haute Couture, simply because his was the first house that had a distinct style that women visited for.
In reality, his clothing designs were sometimes practically mass-produced, it was just extremely high quality textiles, construction, and fitting that separated them. He would sometimes put out dozens of white silk gowns for court wear, needed at the same time, with enough variation in trimmings and exchange of parts that they were "unique". In reality, you might have found quite a few of the same sleeve shape at the event! Even then he kept the parts that still make haute couture distinct today- a specific "look" and high quality.
I don't believe we can consider it to be a British innovation, but to be honest, I don't believe Worth's contributions were as innovative as his reputation suggests.
For audience background: Charles Frederick Worth began working in a draper's shop at the age of twelve, then apprenticed into the textile industry. In 1845, at the age of twenty, he moved to Paris and began working at the Maison Gagelin, where he sold fabric and shawls. He soon married Marie Vernet, the mannequin (live model) in his department, and began to make subdued dresses for her to wear that would help set off the shawls and accessories she wore for display to customers. This led to his being put in charge of a women's clothing department, and eventually he left Gagelin to form Worth & Bobergh with Otto Bobergh in 1858, which he then left in 1870 to form Maison Worth. At his own fashion house, he catered to the very wealthy and built a reputation for quality and arrogance, telling customers what he would make for them rather than taking their orders and declining to take on clients without recommendations. When he died in 1895 the business was inherited by his sons, who ran it jointly - one handling the financial side and one the artistic. The original Parisian house was carried on by two more generations, then sold out to the London branch in 1946, which finally sold the name to a perfumier in the 1950s and closed.
Worth is often credited with creating the concepts of having a shop to sell one's own creations in, designer-set trends, seasonal collections shown in fashion shows, physical labels inside garments, male involvement in dressmaking, and dressmakers not requiring customers to purchase their fabric separately. He's also often considered to have been seen as the most fashionable couturier in the western world during his career, and to have been the primary motivating force in fashion changes during the later 19th century. But the trouble is that a lot of this was established during the early years of fashion history as a discipline and has simply been taken as fact without primary sources.
There are some primary sources that do hold up Worth as the very top of the pyramid (for example, this Manual of Elegant Economy(1859) states that Parisian dress is better than all other fashion because it's directed by masculine taste, and while it describes Worth as "one of these artistic capacities" (emphasis and translation mine), he's the only one named - yet this is evidence that he was not the only established male dressmaker in Paris around the time of the opening of Worth & Bobergh), and he was the main provider of costumes for elaborate court masquerades. But it's a mistake to think of him as operating in a vacuum. Emile Pingat, another very successful couturier, can be found in advertisements for Parisian clothes next to Worth & Bobergh, and other designers and dressmakers whose names are now forgotten were also recommended alongside them.
Certainly the concept of a dressmaker coming up with a particular design that could be had in their shop and advertising it as such was not unique to him - early 19th century fashion magazines, both French and English, published fashion plates at times with notes in the accompanying text that this gown was available in Mrs. Bell's or Mme Hippolyte's shop, and by the 1830s it was fairly common for French publications to point out where each item came from. This plate showing Longchamps fashions notes in the caption that the crepe bonnet trimmed with blonde lace is from the shop of Mme Aubert, while the gros-de-Naples redingote came from Mme Minette's in the rue de Rivoli. Here's another attributing the glazed gros-de-Naples gown to Mme Faulet in the rue St. Joseph. In the 1840s and 1850s the plates became more complex and broke down the parts of the outfit even more - as here, "Hat by Mme Bidault ... Gown by Mlle Eglantine ... Children's clothes by Cior Jr. ... Trims by Bertheley ... Shoes by Dablia ..." or here, "Outfit by Mlle Nathalie ... A la disposition fabric from Maison Deliste ... Child's dress by Mme Leroy ... Perfumes from Legrand ... Fabrics from Villes de France ... Hair jewelry from Lemonnier ..." Name recognition had long been a factor in the Parisian fashion industry.
Worth's early rise has to also be put into perspective with the rise of the department store, which began before he arrived in Paris. One of the advantages of department stores was that a woman's entire ensemble could be produced in-house, without her having to go to one shop to buy fabric and then take it to another to be made up onto a garment (and there is also evidence of some dressmakers in the 18th century controlling both fabric selection and gown creation), so he should also not be credited with the introduction of this concept into the fashion world.
To try to steer myself back on course to your original question - no, I don't believe he brought something specifically British with him. His success seems to have derived in large part from genuinely beautiful design, good business sense, and networking (with a helping of sexism), and then was inflated by the fact that his fashion house did not leave the family or change its name for decades. What he did in terms of the industry was not so much a reformation as it was doing what had been done before on a larger scale and with more grandeur.