  We study the holographic entanglement entropy of an interval in a quantum
field theory obtained by deforming a holographic two-dimensional conformal
field theory via a general linear combination of irrelevant operators that are
closely related to, but nonetheless distinct from, $T{\bar T}, \ J{\bar T}$ and
$T{\bar J}$, and compute the Casin-Huerta entropic $c$-function. We find that
the entropic $c$-function is ultraviolet regulator independent, and along the
renormalization group upflow towards the ultraviolet, it is non-decreasing. We
show that the entropic $c$-function exhibits a power law divergence as the
interval length approaches a minimum finite value determined in terms of the
deformation parameters. We also find for a particular combination of the
deformation parameters a square root correction of the entanglement entropy
area law.
