kindkit expressed an interest in hearing something about the medicalisation of homosexuality in the Victorian era, and I offered to oblige.
Thinking it over, I was not entirely sure that what was happening was medicalisation, because the vast majority of doctors Did Not Want To Know About Icky Sex Stuff of any description (as delineated in an article which is unfortunately not accessible online, L A Hall, '"The English Have Hot Water Bottles": the morganatic marriage between the British medical profession and sexology since William Acton' in Sexual knowledge, sexual science: the history of attitudes to sexuality, edited by Roy Porter and Mikulas Teich, Cambridge University Press, 1994).
True, some of them were approaching the subject of male homosexuality via e.g. forensic medicine, venereology and psychiatric practice. I find that Ivan Crozier's 'The Medical Construction of Homosexuality and its Relation to the Law in Nineteenth-Century England', Medical History, 45, 2001 is freely available via PubMed, and while I do find some of Crozier's work in this area a bit problematic, this is quite a useful contextualisation of the background to Havelock Ellis' work. (Crozier has recently published a critical edition of Ellis's Sexual Inversion. I haven't read the published version.)
However, I think a plausible case can be made that what was going on over the course of the C19th was an endeavour by men who identified as homosexual (or 'inverted' or 'Uranian') to use the resources of science and medicine to construct same-sex desire as a part of nature, a natural thing, rather than 'against nature' or an 'unnatural offence'.
There's a useful website on Karl Ulrichs, the pioneer of this approach.
For more on the thinking that was developing in continental Europe, see Harry Oosterhuis, Stepchildren of Nature: Krafft-Ebing, Psychiatry and the Making of Sexual Identity, University of Chicago Press, 2000. Krafft-Ebing's famous or notorious Psychopathia Sexualis was available in English translation from the early 1890s. I can't recall whether either Watson or Holmes are said to be able to read German (although in Nicholas Meyer's The Seven Per Cent Solution, 1974, movie 1976, Watson takes Holmes to Vienna so that Freud can cure his cocaine habit, I'm not sure of the canonicity of Watson's acquaintance with cutting-edge Continental ideas): there were other works in German e.g. those of Albert Moll. Also some French works.
I would not think it entirely improbable that H&W could have got hold of John Addington Symonds' A Problem in Greek Ethics (1873/1883) and A Problem in Modern Ethics (1891) - although Symonds had these privately printed and disseminated them carefully they were rapidly pirated. Or Edward Carpenter's 1894 Homogenic Love: and its Place in a Free Society (which was left out when the series of essays of which it was part was published as Love's Coming of Age, 1896, though added back into later editions). But these were men of letters/social reformers, even if they were using various scientific studies and theories to support their arguments.
I think H&W might very well have acquired a copy of Havelock Ellis's Sexual Inversion, 1897, possibly even the original edition with Symonds as co-author, which his executors had pulled from sale and destroyed and rewritten to keep Symonds' name out of it out of respect for his widow and children. Ellis was a doctor, but had qualified essentially to give himself cred when researching the psychology of sex, which he considered his life's work. He had a massive knowledge of the contemporary and historical literature on the subject.
What all these were about was toleration and acceptance for the wide diversity of human emotions and affections. I.e not fixing, not curing, but destigmatising and decriminalising. (Krafft-Ebing was a signatory to the petition to repeal the relevant section of the German Penal Code.)
I'm not sure anyone's looked at this in much detail, but my own feeling is that the upsurge of medical attempts to 'cure', whether by hypnosis, hormone treatments, various psychiatric therapies, etc, really only starts manifesting in the C20th, possibly not even until after the Great War (I don't think courts were recommending psychiatric evaluation/treatment until maybe the 1930s, and then only sporadically). It's a while since I've read Forster's Maurice, but as I recollect his family GP totally poohpoohs the idea that a chap like Maurice could be 'an unspeakable of the Oscar Wilde sort' and tells him to go and have a prostitute (this was certainly one thing that was anecdotally prescribed). Though I think he also sees a hypnotist, without much success?
I hope this is some help.