On the basis of high-resolution and high signal-to-noise echelle spectra, some homogeneous atmospheric parameters (T_eff, lgg, V_t, [Fe/H]) for 68 FGK non-variable supergiants and for 26 classical cepheids in 302 pulsation phases were derived with a high accuracy. An extremely high precision of the effective temperature determination (10—30 K) is achieved with the use of the line-depth ratio method. These parameters are correlated with unreddened B-V colour index compiled from the published literature to deduce the empirical relationship in the form: (B - V) ₀ = 57.984 - 10.3587(logT_eff)² + 1.67572( logT_eff)³ - 3.356 logg + 0.0321 V_t + 0.2615[Fe/ H] + 0.8833(logg)( logT_eff). The relationship allows one to estimate intrinsic colours of individual supergiants and classical cepheids with an error of 0.05 mag, which matches the precision of the most sophisticated photometric procedures. The application range is F0-K0 and luminosity classes are I and II. Considering large distances to supergiants, we emphasize that the method described here enables us to make the large-scale extinction mapping of the Galaxy with a sensitivity down to 0.1—0.2 mag.