  In this paper we present results from an IRAM Plateau de Bure millimetre-wave
Interferometer (PdBI) survey for CO emission towards radio-detected
submillimetre galaxies (SMGs) with known optical and near-infrared
spectroscopic redshifts. Five sources in the redshift range z~1-3.5 were
detected, nearly doubling the number of SMGs detected in CO. We summarise the
properties of all 12 CO-detected SMGs, as well as 6 sources not detected in CO
by our survey, and use this sample to explore the bulk physical properties of
the SMG population as a whole. The median CO line luminosity of the SMGs is
<L_CO> = (3.8 +- 2.0) x 10^10 K km/s pc^2. Using a CO-to-H_2 conversion factor
appropriate for starburst galaxies, this corresponds to a molecular gas mass
<M(H_2)> = (3.0 +- 1.6) x 10^10 Msun within a ~2kpc radius, about four times
greater than the most luminous local ultraluminous infrared galaxies (ULIRGs)
but comparable to that of the most extreme high-redshift radio galaxies and
QSOs. The median CO fwhm linewidth is broad, <fwhm> = 780 +- 320 km/s, and the
SMGs often have double peaked line profiles, indicative of either a merger or a
disk. From their median gas reservoirs (~3 x 10^10 Msun) and star-formation
rates (>700 Msun/yr) we estimate a lower limit on the typical gas-depletion
time scale of >40Myr in SMGs. This is marginally below the typical age expected
for the starbursts in SMGs, and suggests that negative feedback processes may
play an important role in prolonging the gas consumption time scale. We find a
statistically-significant correlation between the far-infrared and CO
luminosities of the SMGs which extends the observed correlation for local
ULIRGs to higher luminosities and higher redshifts. [ABRIDGED]
