We estimate cosmological parameters using data obtained by the Very Small Array (VSA) in its extended configuration, in conjunction with a variety of other cosmic microwave background (CMB) data and external priors. Within the flat Λ cold dark matter (ΛCDM) model, we find that the inclusion of high-resolution data from the VSA modifies the limits on the cosmological parameters as compared to those suggested by the Wilkinson Microwave Anisotropy Probe (WMAP) alone, while still remaining compatible with their estimates. We find that Ωbh2= 0.0234+0.0012-0.0014, Ωdmh2= 0.111+0.014-0.016, h= 0.73+0.09-0.05, nS= 0.97+0.06-0.03, 1010AS= 23+7-3 and τ= 0.14+0.14-0.07 for WMAP and VSA when no external prior is included. On extending the model to include a running spectral index of density fluctuations, we find that the inclusion of VSA data leads to a negative running at a level of more than 95 per cent confidence (nrun=-0.069 +/- 0.032), something that is not significantly changed by the inclusion of a stringent prior on the Hubble constant. Inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result by constraining the value of Ωm. We discuss the veracity of this result in the context of various systematic effects and also a broken spectral index model. We also constrain the fraction of neutrinos and find that fν < 0.087 at 95 per cent confidence, which corresponds to mν < 0.32 eV when all neutrino masses are equal. Finally, we consider the global best fit within a general cosmological model with 12 parameters and find consistency with other analyses available in the literature. The evidence for nrun < 0 is only marginal within this model.