  We use the observed polarisation properties of a sample of 26 powerful radio
galaxies and radio-loud quasars to constrain the conditions in the Faraday
screens local to the sources. We adopt the cosmological redshift, low-frequency
radio luminosity and physical size of the large-scale radio structures as our
`fundamental' parameters. We find no correlation of the radio spectral index
with any of the fundamental parameters. The observed rotation measure is also
independent of these parameters. The difference between the rotation measures
of the two lobes of an individual source as well as the dispersion of the
rotation measure show significant correlations with the source redshift, but
not with the radio luminosity or source size. Thus the small-scale structure
observed in the rotation measure is caused by a Faraday screen local to the
sources. The observed asymmetries between the lobes of our sources show no
significant trends with each other or other source properties. Finally, we show
that the commonly used model for the depolarisation of synchrotron radio
emission by foreground Faraday screens is inconsistent with our observations.
We apply alternative models to our data and show that they require a strong
increase of the dispersion of the rotation measure inside the Faraday screens
with cosmological redshift. Correcting our observations with these models for
redshift effects, we find a strong correlation of the depolarisation measure
with redshift and a significantly weaker correlation with radio luminosity. All
our results are consistent with a decrease in the order of the magnetic field
structure of the Faraday screen local to the sources for increasing
cosmological redshift. (abridged)
