We investigate the constraints on basic cosmological parameters set by the first compact-configuration observations of the Very Small Array (VSA), and other cosmological data sets, in the standard inflationary ΛCDM model. Using the weak priors 40 < H0 < 90 km s-1 Mpc-1 and 0 < τ < 0.5, we find that the VSA and COBE-DMR data alone produce the constraints Ωtot= 1.03+0.12-0.12, Ωbh2= 0.029+0.009-0.009, Ωcdmh2= 0.13+0.08-0.05 and ns= 1.04+0.11-0.08 at the 68 per cent confidence level. Adding in the Type Ia supernova constraints, we additionally find Ωm= 0.32+0.09-0.06 and ΩΛ= 0.71+0.07-0.07. These constraints are consistent with those found by the BOOMERanG, DASI and MAXIMA experiments. We also find that, by combining all these cosmic microwave background experiments and assuming the Hubble Space Telescope Key Project limits for H0 (for which the X-ray plus Sunyaev-Zel'dovich route gives a similar result), we obtain the tight constraints Ωm= 0.28+0.14-0.07 and ΩΛ= 0.72+0.07-0.13, which are consistent with, but independent of, those obtained using the supernova data.