We present millimetre photometry and submillimetre imaging of the central c
ore and two hotspots in the radio lobes of the galaxy Cygnus A. For both ho
tspots and the central core, the synchrotron spectrum continues smoothly fr
om the radio to a frequency of 677 GHz. The spectral index of the hotspots
is constant over our frequency range, with a spectral index of alpha approx
imate to -1.0 (S-nu proportional to nu(alpha)), which is steeper than at lo
wer frequencies and represents the emission from an aged population of elec
trons. The core is significantly flatter, with alpha = -0.6 +/- 0.1, sugges
tive of an injected spectrum with no ageing, but some evidence for steepeni
ng exists at our highest observing frequency. Although IRAS data suggest th
e presence of dust in Cygnus A, our 450-mu m data show no evidence of cold
dust, therefore the dust component must have a temperature lying between 85
and 37 K, corresponding to dust masses of 1.4 x 10(6) and 1.0 x 10(8) M. r
espectively.