  We compute the bispectrum induced in the cosmic microwave background (CMB)
temperature and polarisation by the evolution of the primordial density
perturbations using the second-order Boltzmann code SONG. We show that adding
polarisation increases the signal-to-noise ratio by a factor four with respect
to temperature alone and we estimate the observability of this intrinsic
bispectrum and the bias it induces on measurements of primordial
non-Gaussianity. When including all physical effects except the late-time
non-linear evolution, we find for the intrinsic bispectrum a signal-to-noise of
$S/N=3.8,\,2.9,\,1.6$ and $0.5$ for, respectively, an ideal experiment with an
angular resolution of $\ell_\text{max}=3000$, the proposed CMB surveys PRISM
and COrE, and Planck's polarised data; the bulk of this signal comes from the
$E$-polarisation and from squeezed configurations. We discuss how CMB lensing
is expected to reduce these estimates as it suppresses the bispectrum for
squeezed configurations and contributes to the noise in the estimator. We find
that the presence of the intrinsic bispectrum will bias a measurement of
primordial non-Gaussianity of local type by $f_{NL}^\text{bias}=0.66$ for an
ideal experiment with $\ell_\text{max}=3000$. Finally, we verify the robustness
of our results by reproducing the analytical approximation for the
squeezed-limit bispectrum in the general polarised case.
