  The real-space renormalisation group method can be applied to the
Chalker-Coddington model of the quantum Hall transition to provide a convenient
numerical estimation of the localisation critical exponent, $\nu$. Previous
such studies found $\nu\sim 2.39$ which falls considerably short of the current
best estimates by transfer matrix ($\nu\approx 2.593$) and
exact-diagonalisation studies ($\nu=2.58(3)$). By increasing the amount of data
$500$ fold we can now measure closer to the critical point and find an improved
estimate $\nu\approx 2.51$. This deviates only $\sim 3\%$ from the previous two
values and is already better than the $\sim 7\%$ accuracy of the classical
small-cell renormalisation approach from which our method is adapted. We also
study a previously proposed mixing of the Chalker-Coddington model with a
classical scattering model which is meant to provide a route to understanding
why experimental estimates give a lower $\nu\sim 2.3$. Upon implementing this
mixing into our RG unit, we find only further increases to the value of $\nu$.
