Actually, the calender has his name as Aynton, but I think this might be a misprint because, never having heard of him, I did a bit of web searching to find out more. I couldn't find very much about this mysterious man, but his surname does seem most likely to have been Ayton.
According to Wikipedia (not necessarily a more reliable source than Llewellyn's calendar):
"William Alexander Ayton (1816–1909) was a British Anglican clergyman, with an interest in alchemy. He translated from Latin the life of John Dee written by Thomas Smith. He is generally thought to have been a member of the shadowy Society of Eight founded in 1883. He became a member of the successor Order of the Golden Dawn. He was a supporter of the reforms of Arthur Edward Waite, which split the Order as the Holy Order of the Golden Dawn and the Stella Matutina."Another website, Sue Young Homeopathy, states that Ayton was interested in homeopathy as well as alchemy, but was best known as the Golden Dawn's alchemist.
I also found details of a book called The Alchemist of the Golden Dawn: The Letters of the Reverend W.A.Ayton to F.L.Gardener, 1886-1905. Sadly it is out of print. Second hand copies are available through Amazonfor around £35.
Llewellyn's 2010 Witches' Calendar
The Alchemist of the Golden Dawn: The Letters of the Reverend W.A.Ayton to F.L.Gardener, 1886-1905 (Roots of the Golden Dawn series)