A new method is proposed for the formation of MAPbBr3 nanoparticles in situ in a dispersion of polystyrene in toluene in the absence (MAPbBr3@PS) and presence of a broad-band luminophor (MAPbBr3/GAG:Ce@PS). This method permits the lossless use of perovskite, a uniform distribution of the luminophor nanoparticles in the polymer matrix, and maintenance of a high photoluminescence quantum yield (~46%). The samples derived from MAPbBr3 have green photoluminescence with a maximum showing a blue shift in going from bulk perovskite powder to films due to a size effect. The use of nanocomposite films MAPbBr3/GAG:Ce@PS in white LEDs permits enhancement of the color rendering index to 92 with correlation color temperature >5800 K.