It can be difficult to understand the historical approach to dancing when one is used to modern informal dancing, or two-person styles like the waltz or salsa. Yes, people did perform dances all together in lines.

Thoinot Arbeau (Jehan Tabourot) published Orchésographie in 1588, and John Playford published The English Dancing Master, or Plaine and Easy Rules for the Dancing of Country Dances in 1651. (You can find copies of them and more here.) These are two of our earliest sources for what dancing looked like historically, and both describe combinations of basic figures to be performed by a number of dancers at the same time. Arbeau's dances consisted of fairly simple steps - single sideways steps, double sideways steps, kicks, and caprioles (basically, jumping while kicking like mad) - in different combinations, sometimes in circles and sometimes in lines. Playford's encompassed more figures: leading up or down (couples taking hands and dancing/walking "up" or "down" the line), setting (facing the partner in the opposite line and doing some fancy sideways steps), slipping (couples taking both hands and taking sideways steps together), arming (couples taking each other's arms and moving in a circle), and others. That being said, these descriptions of Playford's steps are reconstructions, as he did not define them in his work the way Arbeau did, and we cannot be 100% certain of what Playford meant. Although Playford's book was being issued in new editions pretty regularly until the 1730s, in 1709 John Young revamped it, removing pieces that were too dated and adding new ones that suited modern tastes. Dancing masters who didn't write anything down also existed, of course, and other people went on to write their own treatises on dancing.

By the late 18th century, people were commonly performing country dances (the stereotypical "men in one line, women in another" situation, with the couple at the top of the double line choosing the song and choosing their own figures; as they interacted with the couples below them, those couples would pick up said figures, and eventually both lines would be dancing), cotillions (dances with four couples in two lines, with set steps), and reels (less formal dances); the minuet (a two-person dance) was holding on in instructional books as a way to open a ball, but it was quite archaic.

You wouldn't see a room full of couples dancing outside of these patterns until the waltz, which appeared on the continent and spread to Great Britain in the 1810s. This didn't look exactly like the waltz does today, but it was similar enough to be scandalous - two people clinging to each other for an entire dance! Lord Byron even wrote a poem about how sexy it was. However, dances performed by groups of people together continued to be fashionable and popular: quadrilles, dances for four couples in a square, which had set figures like the cotillion; and a number of dances that were done on the country dance model, in rows and with figures that could be arranged by the head couple or caller/prompter. Quadrilles continued to be popular through the Victorian era, and group game-dances like the "Germans" were soon introduced and popular as well, but by the 1830s couple-dancing had become normal enough for dances involving a "gallop", rushing about in a ballroom hold, to be done without comment. While Germans and quadrilles continued to be performed through to the end of the century, more and more couple dances were added to the fashionable repertoire, and in the early 20th century the concept of groups dancing together socially was killed dead.

So, technically they did not really perform many dances in long lines at Victorian balls, but I think it's possible that you're confusing the Victorian and Regency periods - the Regency was prior to the Victorian period, during the period where Victoria's uncle, George IV, was the regent for his father (1811-1820), and often containing his reign as king as well (1820-1830). Regency fashion involves high waistlines for women and no wigs for men; popular Regency movies are Pride and Prejudice, Sense and Sensibility, and Emma.