Colloidal quantum dots (QDs) are a promising luminescent material for the development of next generation hybrid light-emitting diodes (QDLEDs). In particular, QDs are of great interest in terms of the development of solid-state light sources with an emission spectrum that mimics daylight. In this study, we used CdSe(core)/ZnS/CdS/ZnS(shell) QDs with organic ligands mimicking polyfluorene and its modified derivatives to obtain QD-polymer composites emitting white light. We found that the emission of the composites obtained by spin-coating, being strongly dependent on the chemical structure of the polymer matrix and the QD-to-polymer mass ratio, can be accurately controlled and adjusted to bring its emission spectrum close to the spectrum of daylight (CIE coordinates: 1931 0.307; 0.376). Moreover, the light emission of these composites has been found to be temporally stable, which is due to the minimal structural instability and volume-uniform charge and energy transfer properties. Thus, the use of the synthesized polyfluorene-based organic ligands with controllable chemical structures adaptable to the structure of the polymer matrix can significantly increase the stability of white light emission from QD composites, which can be considered promising electroluminescent materials for fabrication of white QDLEDs.