Context. Rosetta followed comet 67P at heliocentric distances from 1.25 to 3.6 au. The solar wind was observed for much of this time, but was significantly deflected and to some extent slowed down by the interaction with the coma. Aims. We use the different changes in the speed of H+ and He2+ when they interact with the coma to estimate the upstream speed of the solar wind. The different changes in the speed are due to the different mass per charge of the particles, while the electric force per charge due to the interaction is the same. A major assumption is that the speeds of H+ and He2+ were the same in the upstream region. This is investigated. Methods. We derived a method for reconstructing the upstream solar wind from H+ and He2+ observations. The method is based on the assumption that the interaction of the comet with the solar wind can be described by an electric potential that is the same for both H+ and He2+. This is compared to estimates from the Tao model and to OMNI and Mars Express data that we propagated to the observation point. Results. The reconstruction agrees well with the Tao model for most of the observations, in particular for the statistical distribution of the solar wind speed. The electrostatic potential relative to the upstream solar wind is derived and shows values from a few dozen volts at large heliocentric distances to about 1 kV during solar events and close to perihelion. The reconstructed values of the solar wind for periods of high electrostatic potential also agree well with propagated observations and model results. Conclusions. The reconstructed upstream solar wind speed during the Rosetta mission agrees well with the Tao model. The Tao model captures some slowing down of high-speed streams as compared to observations at Earth or Mars. At low solar wind speeds, below 400 km s(-1), the agreement is better between our reconstruction and Mars observations than with the Tao model. The magnitude of the reconstructed electrostatic potential is a good measure of the slowing-down of the solar wind at the observation point.