The Very Small Array (VSA) has been used to survey the l ~ 27° to region of the Galactic plane at a resolution of 13arcmin. This l-range covers a section through the Local, Sagittarius and the Cetus spiral arms. The survey consists of 44 pointings of the VSA, each with an rms sensitivity of ~90mJybeam-1. These data are combined in a mosaic to produce a map of the area. The majority of the sources within the map are HII regions. The main aim of the programme was to investigate the anomalous radio emission from the warm dust in individual HII regions of the survey. This programme required making a spectrum extending from GHz frequencies to the far-infrared (FIR) IRAS frequencies for each of nine strong sources selected to lie in unconfused areas. It was necessary to process each of the frequency maps with the same u, v coverage as was used for the VSA 33GHz observations. The additional radio data were at 1.4, 2.7, 4.85, 8.35, 10.55, 14.35 and 94GHz in addition to the 100, 60, 25 and 12μm IRAS bands. From each spectrum the free-free, thermal dust and anomalous dust emission were determined for each HII region. The mean ratio of 33GHz anomalous flux density to FIR 100μm flux density for the nine selected HII regions was ΔS(33GHz)/S(100μm) = 1.10 +/- 0.21 × 10-4. When combined with six HII regions previously observed with the VSA and the Cosmic Background Imager, the anomalous emission from warm dust in HII regions is detected with a 33GHz emissivity of 4.65 +/- 0.40μK (MJysr-1)-1 (11.5σ). This level of anomalous emission is 0.3 to 0.5 of that detected in cool dust clouds. A radio spectrum of the HII region anomalous emission covering GHz frequencies is constructed. It has the shape expected for spinning dust composed of very small grains. The anomalous radio emission in HII regions is on average 41 +/- 10 per cent of the radio continuum at 33GHz. Another result is that the excess (i.e. non-free-free) emission from HII regions at 94GHz correlates strongly with the 100μm emission; it is also inversely correlated with the dust temperature. Both these latter results are as expected for very large grain dust emission. The anomalous emission on the other hand is expected to originate in very small spinning grains and correlates more closely with the 25μm emission.