Abstract Supernova remnants (SNRs) in Local Group galaxies offer unique insights into the origin of different types of supernovae (SNe). In order to take full advantage of these insights, one must understand the intrinsic and environmental diversity of SNRs in the context of their host galaxies. We introduce a semi-analytic model that reproduces the statistical properties of a radio continuum-selected SNR population, taking into account the detection limits of radio surveys, the range of SN kinetic energies, the measured interstellar medium (ISM) and stellar mass distribution in the host galaxy from multi-wavelength images and the current understanding of electron acceleration and magnetic field amplification in SNR shocks from first-principle kinetic simulations. Applying our model to the SNR population in M33, we reproduce the SNR radio luminosity function with a median SN rate of ∼3.1 × 10−3 per year and an electron acceleration efficiency, εe ∼ 4.2 × 10−3. We predict that the radio visibility times of ∼70 per cent of M33 SNRs will be determined by their Sedov–Taylor lifetimes, and correlated with the measured ISM column density, NH ($t_{\rm {vis}} ∝ N_{\rm H}^{-a}$, with a ∼ 0.33) while the remaining will have visibility times determined by the detection limit of the radio survey. These observational constraints on the visibility time of SNRs will allow us to use SNR catalogues as ‘SN surveys’ to calculate SN rates and delay-time distributions in the Local Group.