In several gamma-ray bursts (GRBs) excess emission, in addition to the standard synchrotron afterglow spectrum, has been discovered in the early-time X-ray observations. It has been proposed that this excess comes from blackbody emission, which may be related to the shock breakout of a supernova in the GRBs progenitor star. This hypothesis is supported by the discovery of excess emission in several GRBs with an associated supernova. Using mock spectra we show that it is only likely to detect such a component, similar to the one proposed in GRB 101219B, at low redshift and in low absorption environments. We also perform a systematic search for blackbody components in all the GRBs observed with the Swift satellite and find six bursts (GRBs 061021, 061110A, 081109, 090814A, 100621A and 110715A) with possible blackbody components. Under the assumption that their excess emission is due to a blackbody component we present radii, temperatures and luminosities of the emitting components. We also show that detection of blackbody components only is possible in a fraction of the Swift bursts.