Oscar Browning (1837-1923) was a fellow of King's College, Cambridge and the co-founder of the Cambridge University Day Training College, where he served as principal between 1891 and 1909.
The narrator is probably quoting from a biography of Oscar Browning by his nephew, H.E. Wortham, entitled: Victorian Eton and Cambridge: being the life and times of Oscar Browning, which was first published in 1927. Alternatively she may be referring to one of two memoirs written by Browning himself: Memories of sixty years at Eton, Cambridge and Elsewhere (1909) and Memoirs of later years (1923).
The significance of the reference to the 'stable-boy lying on the sofa' etc. later on in the text is not made entirely clear, but it appears to be a derogatory reference to Browning's homosexuality.