Like most inventions, the vacuum cleaner did not emerge, whole, out of one inventor's head and immediately attain its perfect form. There were, first, cleaners that used brushes to stir up dust from rugs and cleaners that could be cranked by hand to create suction. There was one that used hand-operated bellows to suck up the dust, and there was one that H. Cecil Booth saw demonstrated in London in 1901 that blew compressed air from two different directions onto a rug.
This was the cleaner that inspired Booth to invent his. He wrote years later in a 1935 journal article on "The Origin of the Vacuum Cleaner" that he had argued with the machine's inventor about its efficacy: "I asked the inventor why he did not suck out the dust… [He] became heated, remarking that sucking out dust was impossible."
Booth supposedly tested that assertion with his mouth, by sucking air from a dusty chair at a restaurant a few days later. It worked—he got a mouthful of dust—although, as Carroll Gantz notes in The Vacuum Cleaner, this may not have been strictly true—or necessary, since "as an accomplished engineer, he would have been quite familiar with the technical principle of creating suction."
Within the year, Booth had designed his own machine, which he called Puffing Billy. It was big and bright red, and would sit outside the building it was cleaning with its pipes snaking inside. In 1902, Puffing Billy was commissioned for a very important job: cleaning out Westminster Abbey before and after the coronation of King Edward VII and Queen Alexandra in 1902.
The Lord Chamberlain was impressed enough with Puffing Billy's performance that he invited Booth to demonstrate his invention before the new monarchs. They liked enough that they bought one for Buckingham Palace and another for Windsor Castle. (Think of all the dust that a normal house collects, then consider the tapestries, rugs, statues, and other dust-collecting surfaces present in very large royal palaces.)
The royal stamp of the approval made Booth's machine trendy. Other European royals wanted one of their own. England's wealthier ladies would host teas during which the vacuum cleaner would suck dust out their houses through glass tubes, so guests could watch. Puffing Billy wasn't the only vacuum cleaner out there, though; in America, Booth's patent application was preceded by another. But Puffing Billy was the only vacuum cleaner endorsed by the British crown—which is at least part of the reason why Booth is often credited as the vacuum cleaner's inventor.