Woodward will surely have met Greek epigram at Harrow, through one of the standard selections compiled for use in classrooms. These books were both teaching tools and paradigms for emulation -- boys not only read but wrote Greek epigrams, and Harrow gave an annual prize for the best such composition. Unsurprisingly, the school selections were carefully winnowed to avoid what we would now term adult content. Published translations into English from the Anthology in the nineteenth century often centred on these poems as familiar mementos of shared upper-class schooldays.
Love-Epigrams knows no such limits, and convinces me that Woodward was choosing his poems from Paton's Loeb, which was still fairly new (1916-18) and was the first and so far the only complete translation of the Anthology into (mostly) English, face-to-face with an affordable and up-to-date edition of its original Greek. Paton's five volumes were a stupendous labour and have been a fundamental resource ever since; an update is under way but has so far only got as far as volume 1.
With Paton to browse in, Woodward ranges widely. The home of heterosexual erotic epigrams is Book 5 of the Anthology, but his selection of 133 poems draws also on Books 6 (votives, x4); 7 (funerary, x2); 9 (epideictic, x7), 10 (protreptic, x1); so-called Book 15 (the Planuedean Appendix, x1); and allegedly also Book 4, though this must be a typo, since Book 4 contains only the prefaces of the anthologists who preceded Cephalas.
By far the largest share of epigrams from outside Book 5, though, comes from Book 12 -- the Anthology's treasure-trove of paederastic epigrams, built around the Mousa Paidikē or 'Boyish Muse' of the notorious Strato of Sardis. One might not expect this from a retired vicar. Woodward's way with the Boyish Muse deserves its own blog post, or posts. Indeed, the very first poem of his selection is one of Strato's.