Reynardine's name (and his initial encounter with Annie) are inspired by the traditional song "Reynardine", which Anne covered.
Winsbury is from the traditional song "Willie O' Winsbury" (interestingly, Kate Rusby also recorded a variant of this song, titled "John Barbury"). In the song, Willie is in a relationship with the king's daughter, Janet, much to the king's displeasure. Replace "king" with "headmaster" and ... yeah.
Lindsey & Bud's names, and the fact that they're engineers in an underwater habitat, to The Abyss.
Tom called Lily "Cookie Monster" when he named her in a tweet. She also shares his color scheme and seemingly has toned-down mannerisms and speech patters of Cookie Monster. She might be also a reference to another Perky GothGenki Girl with much the same colour scheme, perpetual crazy smile and lack of inhibitions in the L.A.W.L.S. comic.
This page might be one to The Lord of the Rings: Sam unhesitatingly grabs Frodo's hand when he's in the "hospital" in front of all their friends (it was kind of a big deal while filming the movie) while Kat hesitates to hold Annie's hand despite (or perhaps because of) the only people around being Robot, Shadow 2, and Reynardine.