  We present new results of a study of the sub-millimetre continuum emission
from a sample of 9 radio galaxies and 4 radio-quiet quasars at redshifts $z =
0.75 - 4.26$. The observations were made at 800$\mu m$, using the
single-element bolometer UKT14 on the James Clerk Maxwell Telescope (JCMT),
reaching a typical r.m.s. sensitivity of $\sigma_{rms} \sim 4$ mJy and
represent some of the deepest submillimetre extragalactic measurements made to
date. Three detections were achieved, of which two are secure (4C41.17, Dunlop
et al. (1994) and H1413$+$117) and one (53W002) is tentative, whilst comparable
upper-limits were obtained for 7 of the 10 remaining sources. We use these data
as the motivation for a detailed discussion of the conversion from
submillimetre and millimetre continuum fluxes to dust/gas masses and star
formation rates at high-redshift, and determine these quantities from our own
and other data on high-redshift radio-galaxies and quasars. In particular we
have investigated the impact of the four main sources of uncertainty in
deriving physical quantities from such data, namely i) potential contamination
by galactic cirrus, ii) uncertainty in the value of the dust rest-frequency
mass-absorption coefficient, iii) difficulty in constraining the dust
temperature, and iv) estimation of the appropriate gas:dust ratio in
high-redshift objects. Our discussion emphasises how important it will be to
quantify and, where possible, minimize such uncertainties (via, for example,
appropriate observational strategies) in order to fully capitalize on the
ten-fold improvement in sensitivity offered by the imminent arrival of the next
generation of bolometer arrays, such as SCUBA on the JCMT.
