[This seems like enough of an answer to post as such, but I still haven't watched the films, so I don't have the full context.]
I watched the Little Witch Academia anime without having seen the films. I didn't have any trouble understanding the plot, and I could spot a major plot twist coming even without the context of the films. However, from the Wikipedia synopses, the events in the two films are not ones that appear in the anime, and at least one plot point is outright handled differently:
Per Wikipedia and the fan wiki, how Akko finds the Shiny Rod is different. In the anime, she stumbles into the Shiny Rod while she is in trouble, while in the film, she finds it on a class assignment to look for treasure.
As far as I can tell, the characterisations in the films and in the anime are consistent with each other. In particular, Akko's incompetence and her classmates' ridicule of her for her love of Shiny Chariot are a theme in both adaptations. Anecdotally, I have also heard that the aforementioned plot twist was foreseeable in the films as well, although it does not appear to be explicitly revealed:
Ursula is Shiny Chariot.