We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low x. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data and robust predictions for future deep inelastic scattering experiments. We find evidence pointing toward a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation to massive quarks.