We present deep radio continuum observations of the cores identified as deeply embedded young stellar objects in the Serpens molecular cloud by the Spitzer c2d programme at a wavelength of 1.8cm with the Arcminute Microkelvin Imager Large Array (AMI-LA). These observations have a resolution of ~30arcsec and an average sensitivity of 19microJy/beam. The targets are predominantly Class I sources, and we find the detection rate for Class I objects in this sample to be low (18%) compared to that of Class 0 objects (67%), consistent with previous works. For detected objects we examine correlations of radio luminosity with bolometric luminosity and envelope mass and find that these data support correlations found by previous samples, but do not show any indiction of the evolutionary divide hinted at by similar data from the Perseus molecular cloud when comparing radio luminosity with envelope mass. We conclude that envelope mass provides a better indicator for radio luminosity than bolometric luminosity, based on the distribution of deviations from the two correlations. Combining these new data with archival 3.6cm flux densities we also examine the spectral indices of these objects and find an average spectral index of 0.53+/-1.14, consistent with the canonical value for a partially optically thick spherical or collimated stellar wind. However, we caution that possible inter-epoch variability limits the usefulness of this value, and such variability is supported by our identification of a possible flare in the radio history of Serpens SMM 1.