  We have mapped four regions of the southern Galactic plane at 31 GHz with the
Cosmic Background Imager. From the maps, we have extracted the flux densities
for six of the brightest \hii regions in the southern sky and compared them
with multi-frequency data from the literature. The fitted spectral index for
each source was found to be close to the theoretical value expected for
optically thin free-free emission, thus confirming that the majority of flux at
31 GHz is due to free-free emission from ionised gas with an electron
temperature of $\approx 7000-8000$ K.
  We also found that, for all six sources, the 31 GHz flux density was slightly
higher than the predicted value from data in the literature. This excess
emission could be due to spinning dust or another emission mechanism.
Comparisons with $100 \mu$m data indicate an average dust emissivity of
$3.3\pm1.7 \mu$K (MJy/sr)$^{-1}$, or a 95 per cent confidence limit of $<6.1
\mu$K (MJy/sr)$^{-1}$. This is lower than that found in diffuse clouds at high
Galactic latitudes by a factor of $\sim 3-4$. The most significant detection
($3.3\sigma$) was found in $G284.3-0.3$ (RCW49) and may account for up to
$\approx 30$ per cent of the total flux density observed at 31 GHz. Here, the
dust emissivity of the excess emission is $13.6\pm4.2 \mu$K (MJy/sr)$^{-1}$ and
is within the range observed at high Galactic latitudes.
  Low level polarised emission was observed in all six sources with
polarisation fractions in the range $0.3-0.6$ per cent. This is likely to be
mainly due to instrumental leakage and is therefore upper an upper limit to the
free-free polarisation. It corresponds to an upper limit of $\sim1$ per cent
for the polarisation of anomalous emission.
