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The Planck list of high-redshift source candidates (the PHz catalogue) contains 2151 peaks in the cosmic infrared background, unresolved by Planck’s 5 arcmin beam. Follow-up spectroscopic observations have revealed that some of these objects are $z\, {\approx }\, 2$ protoclusters and strong gravitational lenses but an unbiased survey has not yet been carried out. To this end, we have used archival Herschel-SPIRE observations to study a uniformly selected sample of 187 PHz sources. In contrast with follow-up studies that were biased towards bright, compact sources, we find that only one of our PHz sources is a bright gravitationally lensed galaxy (peak flux ${\gtrsim }\, 300$ mJy), indicating that such objects are rarer in the PHz catalogue than previously believed (<1 per cent). The majority of our PHz sources consist of many red, star-forming galaxies, demonstrating that typical PHz sources are candidate protoclusters. However, our new PHz sources are significantly less bright than found in previous studies and differ in colour, suggesting possible differences in redshift and star formation rate. None the less, 40 of our PHz sources contain ${\gt }\, 3\, \sigma$ galaxy overdensities, comparable to the fraction of ${\gt }\, 3\, \sigma$ overdensities found in earlier biased studies. We additionally use a machine-learning approach to identify less extreme (peak flux ${\sim }\, 100$ mJy) gravitationally lensed galaxies among Herschel-SPIRE observations of PHz sources, finding a total of seven candidates in our unbiased sample, and 13 amongst previous biased samples. Our new uniformly selected catalogues of ${\gt }\, 3\, \sigma$ candidate protoclusters and strong gravitational lenses provide interesting targets for follow up with higher resolution facilities, such as ALMA and JWST.