Polymeric nanocomposites containing Fe3O4 nanoparticles were prepared through a chemical route under different precursor-to-solvent ratios and were submitted to structural and morphologic characterization. The embedded nanoparticles, containing pure magnetite and characterized by considerable polydispersity, are rather homogeneously dispersed in the matrix. The magnetic properties of two representative samples were analyzed in detail between T=5K and room temperature. Magnetic effects clearly associated with the Verwey monoclinic to cubic transition with transition temperatures distributed in the interval 95-120K were put in evidence. On heating through this region, the coercive field and the maximum susceptibility of hysteresis loops display marked downward/upward steps, respectively, while the high-field magnetization is not affected at all; a comparable upward step is measured in the FC/ZFC curves. Reporting the maximum susceptibility as a function of the reciprocal of the coercive field in the interval from T=95 to T=120K, and using the predictions for single-domain nanoparticles with randomly distributed axes of uniaxial and cubic anisotropy (the former/latter case being applicable below/above the Verwey transition, respectively), the evolution of the transformed cubic-anisotropy fraction upon heating has been studied, and the distribution of Verwey transition temperatures related to the sample polydispersity has been accurately determined. The low-temperature value of the uniaxial anisotropy constant is obtained from coercive field measurements and found to be comparable to, albeit slightly higher than the corresponding quantity measured in bulk crystalline magnetite.