The Cleveland Street Scandal started in 1889, when police discovered a homosexual male brothel on Cleveland Street in London's West Side, made up of largely underage, lower-class male sex workers. The government was accused of covering up the names of aristocrats and other prominent figures that frequented the brothel. The rumors went as high up as Prince Albert Victor, the eldest son of the Prince of Wales and second in-line to the throne. This was never directly proven , but has remained a conspiracy. Lord Arthur Somerset, a major in the Royal Horse Guards and equerry to the Prince of Wales, was also named. He fled to Hamburg, Germany before charges could be brought against him. 

It's important to note that sexual acts between men were illegal at this time in Britain. Oscar Wilde was accused of being tied up in this scandal, but no evidence or proof suggests he partook. One figure that is relevant to the novel did, however. Lord Ronald Gower was well known in the homosexual community at the time, and was publicly implicated in the Cleveland Street Scandal. Gower was a close friend of Wilde's and is portrayed in The Picture Dorian Gray through the character of Lord Henry Wotton. 

Although this scandal did not directly involve Wilde, it did largely influence the conversation surrounding male homosexuality at the time. The scandal was still fresh in the minds of readers by the time The Picture of Dorian Gray was published just one year later, further fueling the idea that male homosexuality was an aristocratic vice that corrupted young, lower-class boys. 

Sources: 

Oscar Wilde, The Picture of Dorian Gray, ed. Joseph Bristow (Oxford: Oxford University Press, 2006).

“The London Scandals .” The Press, 9 Dec. 1889, p. 6, paperspast.natlib.govt.nz/newspapers/CHP18891209.2.40.2.

“The West End Scandal .” Evening News , 14 Jan. 1890, p. 4, trove.nla.gov.au/newspaper/article/108795706?browse=ndp%3Abrowse%2Ftitle%2FE%2Ftitle%2F508%2F1890%2F01%2F14%2Fpage%2F11932216%2Farticle%2F108795706.

Kaczorowski, Craig. “Cleveland Street Scandal .” Glbtq, 2015, www.glbtqarchive.com/ssh/cleveland_street_scandal_S.pdf.