  We develop a method to reconstruct the primordial power spectrum, P(k), using
both temperature and polarisation data from the joint analysis of a number of
Cosmic Microwave Background (CMB) observations. The method is an extension of
the Richardson-Lucy algorithm, first applied in this context by Shafieloo &
Souradeep. We show how the inclusion of polarisation measurements can decrease
the uncertainty in the reconstructed power spectrum. In particular, the
polarisation data can constrain oscillations in the spectrum more effectively
than total intensity only measurements. We apply the estimator to a compilation
of current CMB results. The reconstructed spectrum is consistent with the
best-fit power spectrum although we find evidence for a `dip' in the power on
scales k ~ 0.002 Mpc^-1. This feature appears to be associated with the WMAP
power in the region 18 < l < 26 which is consistently below best--fit models.
We also forecast the reconstruction for a simulated, Planck-like survey
including sample variance limited polarisation data.
