During detailed searches for new Galactic supernova remnants (SNRs) in the Anglo-Australian Observatory/United Kingdom Schmidt Telescope (AAO/UKST) Hα survey of the southern Galactic plane, we also uncovered, for the first time, possible associated Hα emission in the vicinity of about 24 known Galactic SNRs previously known solely from radio or X-ray observations. The possible optical counterparts to these known SNR were detected due to the 1-arcsec resolution and 5 Rayleigh sensitivity of this Hα survey. The newly discovered emission frequently exhibits the typical filamentary form of other optically detected SNRs although sometimes the Hα emission clouds or fragmented filaments largely inside an SNR extend over the radio border. It is true that superposition of general diffuse and extended Galactic emission in the region of these remnants is a complicating factor, but for many optical candidates the Hα emission provides an excellent morphological and positional match to the observed radio emission so that an association seems clear. We have already published Hα images and confirmatory spectral observations for several of the best optical counterparts to known SNRs but for completeness and convenience we include them in our complete catalogue of previously known radio detected SNRs for which we have now uncovered Hα optical emission. For better visualization of the optical emissions from these faint supernova remnants and to enhance some low surface-brightness features we also present quotient images of the Hα data divided by the accompanying broad-band short-red data. Out of 274 Galactic SNRs currently catalogued and detected in the radio only ∼20 per cent had previous optical counterparts. We may have now increased this by a further third by adding a further 24 candidate optical counterparts.