You might be interested in a couple earlier answers on related topics -- for the purposes of this answer I'm going to try and touch on romantic relationships a little more than my usual Ye Olde Cruising answers but there's a ton more to be said about this topic and I would love to read lots of different perspectives on this from other users.
(I'm also going to be pretty freewheeling in my use of "gay" in the following answer -- for most of the century even "homosexual" is anachronistic, so I'm using "gay" in a more expansive sense, also encompassing men we'd now consider to be bisexual/closer to heteroflexible -- men who we might now group under LGBT+, men who had sex with and/or loved men, to whatever degree of exclusivity and regardless of how they conceived of themselves in the language of their time.)
This is one area where the popular impression of gay life is (maybe disproportionately) influenced by one figure -- that of Oscar Wilde and his fate. But Wilde was not the only man in 19th century Britain who had sex with men -- he wasn't even the only one involved in his own trials, for obvious reasons. For alternate narratives of male-male intimacy, adjacent to scandal but not always completely overturned by it, you don't need to go far, and an interested person could look to the biographical details of his friends, his sexual and romantic partners, his blackmailers, or even commentators on the scandal itself.
Why do the Wilde trials have such an outsize legacy, even today? It's not that they aren't hugely significant and notable, or that they aren't in many ways complex and tragic, but they overshadow even other scandals of what we'd now call LGBTQ history of the same era, like the trials of Boulton and Park, and precede accounts of other happier (or at least less conspicuously miserable) gay lives in the same century. It seems likely that this is due to Wilde's own larger-than-life personality as a public figure, and the highly public nature of his condemnation -- ostracized and imprisoned, family life shattered, financially reduced and forced into de facto exile. Even lower-profile homosexual scandals, like the 1872 arrest of Simeon Solomon for attempted sodomy, still held the potential to devastate the professional and personal lives of those caught at their centers. If the social climate alone didn't make the potential hazards of same-sex intimacy clear, the increasingly blunt and forthright coverage of indecent crimes in the popular press would emphasize the same point. This would be enough to fill practically anyone with an awareness of the potential consequences of male-male sexuality, if not out-and-out terror of them. However, Wilde's fate was not unavoidable for any given sexually-active gay man pre-1900 -- even after the scandal had broken in the press and legal action seemed inescapable, friends urged Wilde to relocate to countries on the continent where homosexuality was comparatively better-tolerated, or where the influence of hostile parties might hold less sway. (Outside the British Isles, in colonial holdings and expatriate communities, many white British men led quietly expansive sex lives.) At the same time as Wilde's public humiliation was unfolding, Victorian men were no doubt still meeting and hooking up all over England, and they'd been doing so for decades -- how did they do it? How did they meet?
Public meeting-places provided significant opportunities for casual sex between men, but useful locations like parks and lavatories could be dangerously exposed to law enforcement surveillance as well as violence. Much of my writing about gay men's social lives in the 19th and early 20th century revolves around cruising spots and clandestine gatherings, which is still relevant to your question but doesn't cover the full scope of how men met one another. Men met their lovers through social events in the "straight" world and through family, through work and sport, through organized religion and the arts, at university and in prison -- these associations could cross conventional bounds of race and social class, as in the case of Carpenter and Merrill. Interested men might sound one another out through intuition and insinuation, using subtle conversational hints and shared passions -- these initiatory cues could be as simple as asking for the time of day or for a match to light one's cigarette, or as elaborate as a prolonged courtship. In conversation with close friends or likely-seeming candidates for seduction, men might namedrop famous figures linked with same-sex love and desire, from figures of antiquity like Alexander the Great to moderns like Walt Whitman; in a pinch men could resort to less lofty innuendo in the hope of a positive response, or appeal to face-saving expedience, hoping the object of one's desire was looking to get off and wasn't picky. Circuitous approaches still harbored some level of risk, but they allowed for various degrees of ambiguity and a certain amount of plausible deniability -- striking out at an earlier stage was generally safer than having an actual physical advance rebuffed. Once such a like-minded connection was established, it could be directed into an affair or used as a stepping-stone to a broader gay world. A single connection with homosexual circles (however small and limited those circles were -- as simple as a mutual likeminded friend, for instance) could easily multiply into more. Working-class gay men would have dealt with a distinctly different set of struggles and opportunities, but they were by no means shut out of homosexual subcultures altogether -- working men organized their own drag balls and social clubs, as well as building on associations with men of other social classes to form relationships and have a good time.
It's often easier to envision scandal and misery for men who loved men in this era (imprisonment, blackmail, suicide) than love and happiness, however fleeting, but the two did coexist. A counter-narrative to the Wilde downfall narrative might be that of the working-class George Merrill and his partner, writer and activist Edward Carpenter. The two met in 1891; while Carpenter's outspoken activism in the cause of "homogenic love" attracted personal animosity and occasional police surveillance, the relationship was not characterized by tragedy. The two lived together openly and entertained others their home, including gay notables of the next century like E.M. Forster. The two passed away within a year of each other, after almost four decades of partnership, and were buried in the same grave. This is pretty different from the impression one might get of 19th century gay life from popular media -- as a series of doomed blackmail experiences and chaste caresses culminating in suicide or murder.
As much as I love talking about other gay notables of the era and their sometimes complex love lives, there's no one figure who can really stand in for the breadth of gay experience in this era. The majority of gay men either sought to remain under the radar, or remained under the radar despite themselves; either they successfully skirted the notice of the law, or they circumvented the kind of opprobrium we associate with the legal and social penalties for homosexuality in this era. We know part of how they did it -- through discretion, caution, secrecy, and plausible deniability -- but we also know they employed subterfuge, daring, nervy recklessness, and in some cases simple willingness to break the law and face the consequences as they might come. The nature of much of the documentation of sodomy and gross indecency -- as legal offenses and police matters, recorded on paper and with certain standards for proof -- skews the impression of gay life in the 19th century toward the bleak and the punitive, but that same documentation paired with the richer/more ambiguous material of letters, diaries, and other informal record-keeping can give an impression of a lively, sexually active, and potentially emotionally rewarding existence for men who dared to participate in it.
Successful encounters and relationships, undetected by police and not punished by law, could remain in the realm of the ephemeral, and that makes them somewhat harder to document over a century later. How many men enjoyed same-sex intimacy between 1800 and 1900 in Great Britain and never faced legal prosecution? That's a much harder number to figure than, say, "how many men in Great Britain were tried for gross indecency between 1885 and 1900", or "how many men in Great Britain were charged with sodomy and subsequently acquitted between 18xx and 1900", or other figures where governmental documentation is more likely. Gay men of the 19th century had a remarkably tough row to hoe, still alienated from the relative social and legal acceptance they'd come to find over the 20th and 21st centuries -- however, there's not insignificant evidence that plenty of men made sex and relationships happen with their fellow men without legal consequences, and that others wouldn't let even those consequences stop them.
Some reading:
Nameless Offenses: Speaking of Male Homosexual Desire in Nineteenth-Century England, H.G. Cocks
Strangers, Graham Robb
Masculinity and Male Homosexuality in Britain, 1861-1813, Sean Brady