We constrain the basic comological parameters using the first observations by the Very Small Array ( VSA ) in its extended configuration , together with existing cosmic microwave background data and other cosmological observations . We estimate cosmological parameters for four different models of increasing complexity . In each case , careful consideration is given to implied priors and the Bayesian evidence is calculated in order to perform model selection . We find that the data are most convincingly explained by a simple flat \LambdaCDM cosmology without tensor modes . In this case , combining just the VSA and COBE data sets yields the 68 per cent confidence intervals \Omega _ { b } h ^ { 2 } = 0.034 ^ { +0.007 } _ { -0.007 } , \Omega _ { dm } h ^ { 2 } = 0.18 ^ { +0.06 } _ { -0.04 } , h = 0.72 ^ { +0.15 } _ { -0.13 } , n _ { s } = 1.07 ^ { +0.06 } _ { -0.06 } and \sigma _ { 8 } = 1.17 ^ { +0.25 } _ { -0.20 } . The most general model considered includes spatial curvature , tensor modes , massive neutrinos and a parameterised equation of state for the dark energy . In this case , by combining all recent cosmological data , we find , in particular , 95 percent limit on the tensor-to-scalar ratio R < 0.63 and on the fraction of massive neutrinos f _ { \nu } < 0.11 ; we also obtain the 68 per cent confidence interval w = -1.06 ^ { +0.20 } _ { -0.25 } on the equation of state of dark energy .