We measure the 850-μm source densities of 46 candidate protoclusters selected from the Planck high-z catalogue (PHz) and the Planck Catalogue of Compact Sources (PCCS) that were followed up with Herschel-SPIRE and SCUBA-2. This paper aims to search for overdensities of 850-μm sources in order to select the fields that are most likely to be genuine protoclusters. Of the 46 candidate protoclusters, 25 have significant overdensities (>5 times the field counts), 11 have intermediate overdensities (3–5 times the field counts), and 10 have no overdensity (<3 times the field counts) of 850-μm sources. We find that the enhanced number densities are unlikely to be the result of sample variance. Compared with the number counts of another sample selec...