I think there may also be another source - The White Goddess by Robert Graves, in which he reconstructs/imagines a Celtic 'Tree Alphabet'. According to Graves, in this alphabet 'The seventh tree is the oak'.
For both Garner and Graves, she is a flower/owl goddess with both creative and destructive aspects. For Graves too she is a form of the White Goddess, the poet's muse and source of truth: 'The poet is in love with the White Goddess, with Truth: his heart breaks with longing for her. She is the Flower-goddess Olwen or Blodeuwedd; but she is also Blodeuwedd the Owl, lamp-eyed, hooting dismally, with her foul nest in the hollow of a dead tree'.
Graves also links owls to the Greek myth of the Sirens, enticing sailors to their deaths with their songs: 'Their wings were perhaps owl-wings, since Hesychius mentions a variety of owl called the Siren'.
The Owl Service, and the film The Wicker Man, both embody a recurring urban fantasy: that the British countryside, particularly its Celtic regions, is the home to secret pagan cults surviving from the pre-Christian era (see also Peter Ackroyd's Dorset novel First Light).