We present radio continuum maps of 12 nearby (D<=27Mpc), edge-on (i>=76{deg}), late-type spiral galaxies mostly at 1.4 and 5GHz, observed with the Australia Telescope Compact Array, Very Large Array, Westerbork Synthesis Radio Telescope, Effelsberg 100-m and Parkes 64-m telescopes. All galaxies show clear evidence of radio haloes, including the first detection in the Magellanic-type galaxy NGC 55. In 11 galaxies, we find a thin and a thick disc that can be better fitted by exponential rather than Gaussian functions. We fit our SPINNAKER (SPectral INdex Numerical Analysis of K(c)osmic-ray Electron Radio-emission) 1D cosmic-ray transport models to the vertical model profiles of the non-thermal intensity and to the non-thermal radio spectral index in the halo. We simultaneously fit for the advection speed (or diffusion coefficient) and magnetic field scale height. In the thick disc, the magnetic field scale heights range from 2 to 8kpc with an average across the sample of 3.0+/-1.7kpc; they show no correlation with either star-formation rate (SFR), SFR surface density (Sigma_SFR_) or rotation speed (V_rot_). The advection speeds range from 100 to 700km/s and display correlations of V{prop.to}SFR^0.36+/-0.06^ and V{prop.to}Sigma_SFR_^0.39+/-0.09^; they agree remarkably well with the escape velocities (0.5<=V/V_esc<=2), which can be explained by cosmic-ray driven winds. Radio haloes show the presence of disc winds in galaxies with Sigma_SFR_>10^-3^M_{sun}_/yr/kpc^2^ that extend over several kpc and are driven by processes related to the distributed star formation in the disc.