It's pretty widely considered an old Victorian-era urban legend at this point, and some kind of sensational Boogeyman story. The first attacks (allegedly) took place in Lavender Hill where your typically Rapey Groperson MO played out, except that Mr. Groperson (allegedly) leapt straight over a carriage and then over a 9-ft wall before disappearing.
Some accounts say that he spat blue flames and had glowing red eyes and all kinds of other crazy monster traits but those are widely acknowledged to be fanciful imaginings.
It was serious enough at the time that the Mayor of London was willing to at least partially acknowledge the goings on (admitting the attacks had happened, but not that Groperson McCreepy was any kind of literal monster) and the Duke of Wellington took to patrolling his neighborhood at night to protect young women. The character seeped into the public consciousness and had starring roles in Penny Dreadfuls and Punch and Judy puppet shows for decades.
If even half the stories are to be believed, he traveled all over the country scaring the willies out of women and children, pestering security guards, kicking dogs, and generally being a right bastard and a nuisance from 1837 until the last reported sighting in 1904.
Here are some artists renderings, and if you're incredibly fortunate you might be able to dig up some of the Times articles on the attacks as well.