  We derive constraints on cosmological parameters using the power spectrum of
galaxy clustering measured from the final two-degree field galaxy redshift
survey (2dFGRS) and a compilation of measurements of the temperature power
spectrum and temperature-polarization cross-correlation of the cosmic microwave
background radiation. We analyse a range of parameter sets and priors, allowing
for massive neutrinos, curvature, tensors and general dark energy models. In
all cases, the combination of datasets tightens the constraints, with the most
dramatic improvements found for the density of dark matter and the
energy-density of dark energy. If we assume a flat universe, we find a matter
density parameter of $\Omega_{\rm m}=0.237 \pm 0.020$, a baryon density
parameter of $\Omega_{\rm b} = 0.041 \pm 0.002$, a Hubble constant of
$H_{0}=74\pm2 {\rm kms}^{-1}{\rm Mpc}^{-1}$, a linear theory matter fluctuation
amplitude of $\sigma_{8}=0.77\pm0.05$ and a scalar spectral index of $n_{\rm
s}=0.954 \pm 0.023$ (all errors show the 68% interval). Our estimate of $n_{\rm
s}$ is only marginally consistent with the scale invariant value $n_{\rm s}=1$;
this spectrum is formally excluded at the 95% confidence level. However, the
detection of a tilt in the spectrum is sensitive to the choice of parameter
space. If we allow the equation of state of the dark energy to float, we find
$w_{\rm DE}= -0.85_{-0.17}^{+0.18}$, consistent with a cosmological constant.
We also place new limits on the mass fraction of massive neutrinos: $f_{\nu} <
0.105$ at the 95% level, corresponding to $\sum m_{\nu} < 1.2$ eV.
