We present a spectroscopic catalogue of 40 luminous starburst galaxies at z= 0.7–1.7 (median z= 1.3). 19 of these are submillimetre galaxies (SMGs) and 21 are submillimetre-faint radio galaxies (SFRGs). This sample helps us to fill in the redshift desert at z= 1.2–1.7 in previous studies as well as to probe a lower luminosity population of galaxies. Radio fluxes are used to determine star formation rates for our sample which range from around 50–500 M⊙ yr−1 and are generally lower than those in z∼ 2 SMGs. We identify nebular [O ii] 3727 emission in the rest-UV spectra and use the linewidths to show that SMGs and SFRGs in our sample have larger linewidths and therefore dynamical masses than optically selected star-forming galaxies at similar redshifts. The linewidths are indistinguishable from those measured in the z∼ 2 SMG populations suggesting little evolution in the dynamical masses of the galaxies between redshift 1 and 2. [Ne v] and [Ne iii] emission lines are identified in a subset of the spectra indicating the presence of an active galactic nucleus (AGN). In addition, a host of interstellar absorption lines corresponding to transitions of Mg ii and Fe ii ions are also detected. These features show up prominently in composite spectra and we use these composites to demonstrate that the absorption lines are present at an average blueshift of −240 ± 50 km s−1 relative to the systemic velocities of the galaxies derived from [O ii]. This indicates the presence of large-scale outflowing interstellar gas in these systems. We do not find any evidence for differences in outflow velocities between SMGs and SFRGs of similar infrared luminosities. We find that the outflow velocities of z∼ 1.3 SMGs and SFRGs are consistent with the V∝ SFR0.3 local envelope seen in lower redshift ultraluminous infrared galaxies (ULIRGs). These observations are well explained by a momentum-driven wind model