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Within the framework of the dipole factorisation, we use a recent collinearly-improved version of the Balitsky-Kovchegov equation to fit the HERA data for inclusive deep inelastic scattering at small Bjorken x. The equation includes an all-order resummation of double and single transverse logarithms and running coupling corrections. Compared to similar equations previously proposed in the literature, this work makes a direct use of Bjorken x as the rapidity scale for the evolution variable. We obtain excellent fits for reasonable values for the four fit parameters. We find that the fit quality improves when including resummation effects and a physically-motivated initial condition. In particular, the resummation of the DGLAP-like single transverse logarithms has a sizeable impact and allows one to extend the fit up to relatively large photon virtuality Q2.