We present results from observations made at 33 GHz with the Very Small Array (VSA) telescope towards potential candidates in the Galactic plane for spinning dust emission. In the cases of the diffuse HII regions LPH96 and NRAO591 we find no evidence for anomalous emission and, in combination with Effelsberg data at 1.4 and 2.7GHz, confirm that their spectra are consistent with optically thin free-free emission. In the case of the infrared bright supernova remnant 3C396 we find emission inconsistent with a purely non-thermal spectrum and discuss the possibility of this excess arising from either a spinning dust component or a shallow spectrum pulsar wind nebula, although we conclude that the second case is unlikely given the strong constraints available from lower-frequency radio images.