  We constrain flat cosmological models with a joint likelihood analysis of a
new compilation of data from the cosmic microwave background (CMB) and from the
2dF Galaxy Redshift Survey (2dFGRS). Fitting the CMB alone yields a known
degeneracy between the Hubble constant h and the matter density Omega_m, which
arises mainly from preserving the location of the peaks in the angular power
spectrum. This `horizon-angle degeneracy' is considered in some detail and
shown to follow a simple relation Omega_m h^{3.4} = constant. Adding the 2dFGRS
power spectrum constrains Omega_m h and breaks the degeneracy. If tensor
anisotropies are assumed to be negligible, we obtain values for the Hubble
constant h=0.665 +/- 0.047, the matter density Omega_m=0.313 +/- 0.055, and the
physical CDM and baryon densities Omega_c h^2 = 0.115 +/- 0.009, Omega_b h^2 =
0.022 +/- 0.002 (standard rms errors). Including a possible tensor component
causes very little change to these figures; we set a upper limit to the
tensor-to-scalar ratio of r<0.7 at 95% confidence. We then show how these data
can be used to constrain the equation of state of the vacuum, and find w<-0.52
at 95% confidence. The preferred cosmological model is thus very well
specified, and we discuss the precision with which future CMB data can be
predicted, given the model assumptions. The 2dFGRS power-spectrum data and
covariance matrix, and the CMB data compilation used here, are available from
http://www.roe.ac.uk/~wjp/
