We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18yr. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TEMPONEST yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semimajor axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler. However, we measure an average uncertainty of 80 per cent (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J1600-3053 and J1918-0642, implying pulsar and companion masses mp=1.22^+0.5^_-0.35_M_{sun}_, mc=0.21^+0.06^_-0.04_M_{sun}_ and mp=1.25^+0.6^_-0.4_M_{sun}}, mc=0.23^+0.07^_-0.05_M_{sun}_, respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J1012+5307 and J1909-3744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J1600-3053 and J1909-3744.