First of all, let me say that I find what is happening at Leicester utterly horrible.
However, the truth is that pure mathematicians do, in general, tend to have a disdain for applied work. In not a few places "mathematics departments", which originally contained within them areas such as statistics or computer science, tended to eject any type of applied field and let them create their own departments, while leaving only the purest of the purest within the administrative division labelled "mathematics". This attitude is now coming back to bite them.
As a long-term strategy, it might serve mathematics departments well to maintain more diversity in their research focus, and not segregate "pure" and "applied" research. After all, there isn't really a very clear line between "pure" and "applied": a single researcher may do some of both, and some types of research touch on both. If the University of Leicester did not have two clearly separated administrative divisions labelled "pure math" and "applied math", then they could not pull this off.
This is not meant as criticism, but as a pragmatic suggestion.