Opinions vary as to when dance cards came into popular in England. While I can’t find evidence that they were used in England during the Regency era, they appear to have been made in Birmingham, England as early as 1803. According to my research, Austrians used dance cards before they caught on in the rest of Europe. Later, dance cards probably spread as people returned home from the Congress of Vienna which was basically a big party disguised as a series of series of negotiations that officially ended the Napoleonic Wars (David King’s Vienna 1814 is a great source for The Congress). Dance cards gained popularity at balls and assemblies sometime during the 1830s, during Queen Victoria's reign.
A few are inscribed with the words "Bal" which is French for ball. The ones with images I could use look like fans, others I saw are booklets with ornate covers.
Anyway, at the time of the Vienna Conference, country dancing and formal minuets began losing popularity. Precedence and etiquette which dictated to whom one could dance had begun to fade, and the long country dances were replaced by shorter pair dances like the waltz, valse, polka, lancers and quadrille. Because of the new, less formal dancing and shorter dances, people could do more of them each evening. It probably became harder for young ladies to remember which young gentleman she'd promised a dance. Some sources mention ladies writing names on the underside of their fans to help them remember promised dances but I don't know how often or when that occurred. At one point, ladies reportedly used decorative notebooks to keep track of the name of each gentleman who'd asked for her to "stand up" with him. Many ladies already carried in their reticules small notebooks that opened like fans to jot down shopping lists and so forth. Naturally, they used them to record their evening's dance partners. Many preserved them as a souvenir of the evening.
Later in the century, dance cards became pre-printed booklets of paper which listed each dance the musicians would play, in order. They became progressively more decorative and elaborate as the century progressed. Ribbon or cord attached tiny pencils to the card or program by which ladies let the cards dangle from their wrist. Some were metal, others were made of shells or carved bone.
Fellow Regency author, Marissa Doyle, has a wonderful collection of dance cards in her private collection. You can view her post on Dance Cards, and admire her pictures, here on her blog, Nineteen Ten.
As far as I can tell, dance cards began to lose popularity sometime in the 1920s. Of course, now, no one reserves dances and few even know how to dance. Sigh. Too bad.
So anyway, if you've ever wondered why I never use dance cards in my Regency historical romance novels, now you know. They didn't appear to have existed in Regency England.