We present adaptive optics assisted, spatially resolved spectroscopy of a sample of nine Hα-selected galaxies at z = 0.84–2.23 drawn from the HiZELS narrow-band survey. These galaxies have star formation rates of 1–27 M⊙ yr−1 and are therefore representative of the typical high-redshift star-forming population. Our ∼kpc-scale resolution observations show that approximately half of the sample have dynamics suggesting that the ionized gas is in large, rotating discs. We model their velocity fields to infer the inclination-corrected, asymptotic rotational velocities. We use the absolute B-band magnitudes and stellar masses to investigate the evolution of the B-band and stellar-mass Tully–Fisher relationships. By combining our sample with a number of similar measurements from the literature, we show that, at fixed circular velocity, the stellar mass of star-forming galaxies has increased by a factor of 2.5 between z = 2 and 0, whilst the rest-frame B-band luminosity has decreased by a factor of ∼ 6 over the same period. Together, these demonstrate a change in mass-to-light ratio in the B band of Δ(M/LB)/(M/LB)z=0 ∼ 3.5 between z = 1.5 and 0, with most of the evolution occurring below z = 1. We also use the spatial variation of [N ii]/Hα to show that the metallicity of the ionized gas in these galaxies declines monotonically with galactocentric radius, with an average Δ log(O/H)/ΔR = −0.027 ± 0.005 dex kpc−1. This gradient is consistent with predictions for high-redshift disc galaxies from cosmologically based hydrodynamic simulations.