One of the problems of searching for him is that the name is often not listed right -
A Peruvian, Eliseo Abelardo Alvarez-Calderon was the Principal of St. John's Wood. The two artists were not related. A place to look for information on Abelardo and the school is the Books section of Google, which holds some contemporary 19th/early 20th century references for the school. Sadly, not much info or Abelardo, or his work, is on the internet: the teachers get lost...the location was indeed 9 Elm Tree Road.
Have you seen this article? This one is the best: It contains a family history (including scandal!) and a portrait Abelardo did of his wife.
Alvarez-CalderonPhilip, from France, was involved with the St. John's clique that preceded the school.