We study ternary mixtures of nonionic surfactants CiEj (i = 12; j = 5, 6, 8) and poly(ethylene glycol) (PEG) in water. For sufficiently large molecular mass of PEG (M > M-sep similar to 600), we observe a lowering of phase separation temperature with an increase in polymer concentration. The value of M-sep is consistent with the analysis based on depletion interactions between micelles induced by polymer chains. We also demonstrate that there is another critical molecular mass of PEG (M = M* similar to 2000) necessary to induce ordering in the surfactant-rich phase. This critical molecular mass follows from two requirements: (a) PEG has to reduce the separation temperature below a temperature of hexagonal-isotropic phase transition in a binary surfactant-water mixture and (b) the PEG radius of gyration has to be larger than the size of the water channels in the hexagonal phase.