  We present VSA observations (~34GHz) on scales ~20 arcmin towards a complete,
X-ray-flux-limited sample of seven clusters at redshift z<0.1. Four have
significant SZ detections in the presence of CMB primordial anisotropy. We use
a bayesian MCMC method for inference from the VSA data, with X-ray priors on
cluster positions and temperatures, and radio priors on sources. We make
assumptions of beta-model gas distributions and of hydrostatic equilibrium, to
evaluate probability densities for the gas mass and total mass out to r_200.
Our combined estimate of the gas fraction is 0.08^{+0.06}_{-0.04}h^{-1} The
random errors are poor (note that the errors are higher than would have been
obtained with the usual chi-squared method) but the control of bias is good. We
have described the MCMC analysis method specifically in terms of SZ but hope
the description will be of more general use. We find that the effects of
primordial CMB contamination tend to be similar in the estimates of both the
gas mass and total mass over our narrow range of angular scales, so that there
is little effect of primordials on the gas fraction determination. Using our
total mass estimates we find a normalisation of the mass-temperature relation
based on the profiles from the VSA cluster pressure maps that is in good
agreement with recent M-T determinations from X-ray cluster measurements.
