  We present results from a Monte Carlo simulation of non-compact lattice QED
in 3 dimensions on a $16^3$ lattice in which an explicit anisotropy between $x$
and $y$ hopping terms has been introduced into the action. This formulation is
inspired by recent formulations of anisotropic QED$_3$ as an effective theory
of the non-superconducting portion of the cuprate phase diagram, with
relativistic fermion degrees of freedom defined near the nodes of the gap
function on the Fermi surface, and massless photon degrees of freedom
reproducing the dynamics of the phase disorder of the superconducting order
parameter. Using a parameter set corresponding to broken chiral symmetry in the
isotropic limit, our results show that the renormalised anisotropy, defined in
terms of the ratio of correlation lengths of gauge invariant bound states in
the $x$ and $y$ directions, exceeds the explicit anisotropy $\kappa$ introduced
in the lattice action, implying in contrast to recent analytic results that
anisotropy is a relevant deformation of QED$_3$. There also appears to be a
chiral symmetry restoring phase transition at $\kappa_c\simeq4.5$, implying
that the pseudogap phase persists down to T=0 in the cuprate phase diagram.
