We present molecular line observations made with the IRAM 30-m telescope of the immediate surroundings of a sample of 11 candidate high-mass protostars . These observations are part of an effort to clarify the evolutionary status of a set of objects which we consider to be precursors of UC H ii regions . In a preceding series of papers we have studied a sample of objects , which on the basis of their IR colours are likely to be associated with compact molecular clouds . The original sample of 260 objects was divided approximately evenly into a High group , with IR colour indices [ 25–12 ] \geq 0.57 and [ 60–12 ] \geq 1.3 , and a Low group with complementary colours . The FIR luminosity of the Low sources , their distribution in the IR colour-colour diagram , and their lower detection rate in H _ { 2 } O maser emission compared to the High sources , led to the hypothesis that the majority of these objects represent an earlier stage in the evolution than the members of the High group , which are mostly identifyable with UC H ii regions . Subsequent observations led to the selection of 12 Low sources that have FIR luminosities indicating the presence of B2.5 to O8.5 V _ { 0 } stars , are associated with dense gas and dust , have ( sub- ) mm continuum spectra indicating temperatures of \sim 30 K , and have no detectable radio continuum emission . One of these sources has been proposed by us to be a good candidate for the high-mass equivalent of a Class 0 object . In the present paper we present observations of the molecular environment of 11 of these 12 objects , with the aim to derive the physical parameters of the gas in which they are embedded , and to find further evidence in support of our hypothesis that these sources are the precursors to UC H ii regions . We find that the data are consistent with such an interpretation . All observed sources are associated with well-defined molecular clumps . Masses , sizes , and other parameters depend on the tracer used , but typically the cores have average diameters of \sim 0.5–1 pc ( with a range of 0.2 to 2.2 pc ) , and masses of a few tens to a few thousand solar masses . Compared to a similar analysis of High sources , the present sample has molecular clumps that are more massive , larger , cooler , and less turbulent . They also tend to have a smaller ratio of virial-to-luminous mass , indicating they are less dynamically stable than their counterparts in which the High sources are embedded . The large sizes suggest these clumps should still undergo substantial contraction ( their densities are \sim 10 times smaller than those of the High sources ) . The lower temperatures and small linewidths are also expected in objects in an earlier evolutionary state . In various sources indications are found for outflowing gas , though its detection is hampered by the presence of multiple emission components in the line spectra . There are also signs of self-absorption , especially in the spectra of ^ { 13 } CO and HCO ^ { + } . We find that the masses of the molecular clumps associated with our objects increase with L _ { fir } ( M _ { clump } \propto L _ { fir } ^ { 1.17 } ) , and that there is a ( weak ) relation between the clump mass and the mass of the embedded protostellar object M _ { proto } \propto M _ { clump } ^ { 0.30 } . The large amount of observational data is necessarily presented in a compact , reduced form . Yet we supply enough information to allow further study . These data alone can not prove or disprove the hypothesis that among these objects a high-mass protostar is truly present . More observations , at different wavelenghts and spatial resolutions are needed to provide enough constraints on the number of possible interpretations .