  Context. B-type supergiants are versatile tools to address various
astrophysical topics, ranging from stellar atmospheres over stellar and
galactic evolution to the cosmic distance scale. Aims. A hybrid non-LTE
approach - line-blanketed model atmospheres computed under the assumption of
local thermodynamic equilibrium (LTE) in combination with line formation
calculations that account for deviations from LTE - is tested for quantitative
analyses of B-type supergiants with masses $M<30 M_{\odot}$, characterising a
sample of 14 Galactic objects. Methods. Hydrostatic plane-parallel atmospheric
structures and synthetic spectra computed with Kurucz's Atlas12 code together
with the non-LTE line-formation codes Detail/Surface are compared to results
from full non-LTE calculations with Tlusty, and the effects of turbulent
pressure on the models are investigated. High-resolution spectra are analysed
for atmospheric parameters, using Stark-broadened hydrogen lines and multiple
metal ionisation equilibria, and for elemental abundances. Fundamental stellar
parameters are derived by considering stellar evolution tracks and Gaia EDR3
parallaxes. Interstellar reddening towards the target stars is determined by
matching model spectral energy distributions to observed ones. Results. Our
hybrid non-LTE approach turns out to be equivalent to hydrostatic full non-LTE
modelling for the deeper photospheric layers of the B-type supergiants
considered. Turbulent pressure can become relevant for microturbulent
velocities larger than 10 km s$^{-1}$. High precision and accuracy is achieved
for all derived parameters by bringing multiple indicators to agreement
simultaneously. Abundances for chemical species (He, C, N, O, Ne, Mg, Al, Si,
S, Ar, Fe) are derived with uncertainties of 0.05 to 0.10 dex. The derived
ratios N/C vs. N/O tightly follow the predictions from Geneva stellar evolution
models.
