'Hooligans' first appeared in the 1890s. Previously they were called 'roughs' or 'thugs' and 'Hooligan' was just an Irish surname; then the word somehow acquired the modern meaning.
Clarence Rook's The Hooligan Nights (1899), purporting to be a factual account of the London underworld, contemplates a sample 'hooligan' in Lambeth, by the name of Alf. His book doesn't quite read like a straight documentary account; and one suspects - simply because its so artfully done - that it's substantially fiction. Rook does, however, provide an explanation for the word's origin:
"There, was, but a few years ago, a man called Patrick Hooligan, who walked to and fro among his fellow-men, robbing them and occasionally bashing them. This much is certain. His existence in the flesh is a fact as well established as the existence of Buddha or of Mahomet. But with the life of Patrick Hooligan, as with the lives of Buddha and of Mahomet, legend has been at work, and probably many of the exploits associated with his name spring from the imagination of disciples. It is at least certain that he was born, that he lived in Irish Court, that he was employed as a chucker-out at various resorts in the neighbourhood."
I strongly suspect this also is pure fiction. I can't find this man in the press, certainly not in the early articles which use the word; and Rook's comparison to Buddha or Mahomet is protesting just a little too much. The next thing, of course, is to consult the OED:
The OED is not quite right, however - and I know this only because of the new British Library press database. I've put the articles here - what it shows is that the first 'hooligans' were a distinct gang in Lambeth in 1894 who called themselves the 'Hooligan boys'. This follows a music-hall song called the 'O'Hooligan Boys' which was being performed nearby in 1891; and one is inclined to think that is where they got the name. The phrase then got generalised - a 'masher' in Paddington (nowhere near Lambeth) is called a 'member of the Hooligan gang' in 1895 - until we have 'hooligan girls' who push and punch another girl in 1898.
"The word first appears in print in daily newspaper police-court reports in the summer of 1898. Several accounts of the rise of the word, purporting to be based on first-hand evidence, attribute it to a misunderstanding or perversion of Hooley or Hooley's gang, but no positive confirmation of this has been discovered. The name Hooligan figured in a music-hall song of the eighteen-nineties, which described the doings of a rowdy Irish family, and a comic Irish character of the name appeared in a series of adventures in Funny Folks."
In short, looking through the press reports, the phrase clearly describes a particular group of young men in 1894. The specificity to Lambeth, and that particular group is gradually lost, as more shocking stories of 'hooliganism' appear (often not much different from regular crimes, to tell the truth). There is, admittedly, a particular flare-up of violence in Lambeth in 1898, which attracts the 'hooligan' tag - and more press attention to the area. But soon it appears 'hooliganism' is everywhere, not just darkest South London.
Interestingly, some of the offences ascribed to 'hooligan gangs' are serious - murder and threatening witnesses - whilst some are trivial (knocking hats off people's heads, for instance) but the tag of 'hooligan' fits all. British residents can compare and contrast with the modern 'hoodie' paranoia, or any moral panic in the last two hundred years. There were, of course, plenty of criminals in Lambeth - but how many were 'hooligans'?
The moral, if any, is that the press - the media - the public - love neat labels?