  The high-magnification gravitational lensing cross-section of a galaxy is
enhanced significantly if a baryonic disc is embedded in its dark matter halo.
We investigate the effects of a population of such disks on the probability of
detecting strongly lensed images of distant galaxies and quasars. The optical
depth to lensing is always more than doubled. The effects are particularly
significant at magnifications greater than about 50, for which the optical
depth typically increases by a factor greater than 5. If either the fraction of
discs or the typical disc-to-halo mass ratio increases with redshift, then the
optical depth is expected to be increased even further. Obscuration by dust in
the lensing disc is expected to counteract the associated enhanced
magnification bias for surveys in the optical waveband, but not in the radio
and millimetre/submillimetre wavebands. The presence of galactic discs should
hence lead to a significant increase in the number of lensed galaxies and
quasars detected in both radio- and millimetre/submillimetre-selected surveys.
An increase by a factor of about 3 is expected, enhancing the strong case for
millimetre/submillimetre-wave lens surveys using the next generation of
ground-based telescopes and the FIRST and Planck Surveyor space missions.
