  While the theory of labelled well-quasi-order has received significant
attention in the graph setting, it has not yet been considered in the context
of permutation patterns. We initiate this study here, and show how labelled
well quasi order provides a lens through which to view and extend previous
well-quasi-order results in the permutation patterns literature. Connections to
the graph setting are emphasised throughout. In particular, we establish that a
permutation class is labelled well-quasi-ordered if and only if its
corresponding graph class is also labelled well-quasi-ordered.
