How prevalent was homosexuality at British public schools?

Very, in the nineteenth century. As early as the 1830s, British journals and magazines were reporting on what they called 'immorality'--a code word for romantic and/or sexual relationships, though it could also mean masturbation or general lewdness--among public school boys.

On 12 May 1895 (incidentally, this was just thirteen days before Oscar Wilde would be convicted on charges of gross indecency), Reynolds's Newspaper in London ran a letter to the editor titled 'Immorality at Public Schools' in which 'A Schoolboy' writes:

In all public schools, without exception, the elements of vice are grafted into the delicate frames of the unhappy wights of those institutions.

It should be noted that 'Schoolboy' explicitly mentions masturbation, pornography and sexual talk among the boys at his unnamed school, but remains silent on romances among the students. Perhaps 'Schoolboy' genuinely never saw such relationships, but perhaps he did and thought better of writing about them, as 'any act of gross indecency with an other male person' had been made illegal by the Labouchere Amendment in 1885. In any case, public schools were hotbeds of sexual activity, whether masturbatory or interpersonal.

John Addington Symonds wrote in his Memoirs about his experiences at Harrow:

Every boy of good looks had a female name, and was recognised either as a public prostitute or as some bigger fellow's 'bitch.' Bitch was the word in common usage to indicate a boy who yielded his person to a lover.

It wasn't just Harrow, either. Lord Alfred Douglas (aka 'Bosie'), famous for being one of Oscar Wilde's lovers, attended Winchester and referred to it as a 'sink of iniquity' where 'at least ninety per cent' of his fellow schoolboys were having sex with other students. Not that Bosie was opposed to all the sex among students, after he acclimated to the school. 'I got used to the conditions,' he wrote, 'adapted myself to the standard of morality--or rather immorality--and enjoyed the whole thing immensely.'

Sex among the boys was common enough at Winchester that there seems to have been a fairly reified hierarchy of the 'badness' of various acts and appropriate ways of punishing the students who got caught. Edmund Trelawny Backhouse estimated that at least twenty boys were expelled from Winchester for anal sex or intercural sex during his six years there. Mutual masturbation was punishable, too, but not as severely: offenders would not be expelled, but rather beaten.

Sources:

'Immorality at Public Schools', Reynolds's Newspaper, 12 May 1895, p. 2

McKenna, Neil, The Secret Life of Oscar Wilde (New York: Basic Books, 2005)

Symonds, John Addington, The Memoirs of John Addington Symonds, ed. by Phyllis Grosskurth (London: Hutchinson, 1984)