The Balmer lines of four A Ia-supergiants (spectral type A0 to A3) and fourteen B Ia and Ib-supergiants (spectral type B0 to B3) in the solar neighbourhood are analyzed by means of NLTE unified model atmospheres to determine the properties of their stellar winds, in particular their wind momenta. As in previous work for O-stars (Puls et al. cite{pul96}) a tight relationship between stellar wind momentum and luminosity (``WLR'') is found. However, the WLR varies as function of spectral type. Wind momenta are strongest for O-supergiants, then decrease from early B (B0 and B1) to mid B (B1.5 to B3) spectral types and become stronger again for A-supergiants. The slope of the WLR appears to be steeper for A- and mid B-supergiants than for O-supergiants. The spectral type dependence is interpreted as an effect of ionization changing the effective number and the line strength distribution function of spectral lines absorbing photon momentum around the stellar flux maximum. This interpretation needs to be confirmed by theoretical calculations for radiation driven winds. The ``Pistol-Star'' in the Galactic Centre, an extreme mid B-hypergiant recently identified as one of the most luminous stars (Figer et al. cite{fig99}) is found to coincide with the extrapolation of the mid B-supergiant WLR towards higher luminosities. However, the wind momentum of the Luminous Blue Variable P Cygni, a mid B-supergiant with extremely strong mass-loss, is 1.2 dex higher than the WLR of the ``normal'' supergiants. This significant difference is explained in terms of the well-known stellar wind bi-stability of supergiants very close to the Eddinton-limit in this particular range of effective temperatures. A-supergiants in M31 observed with HIRES at the Keck telescope have wind momenta compatible with their galactic counterparts. The potential of the WLR as a new, independent extragalactic distance indicator is discussed. It is concluded that with ten to twenty objects, photometry with HST and medium resolution spectroscopy with 8m-telescopes from the ground distance moduli can be obtained with an accuracy of about 0fm1 out to the Virgo and Fornax clusters of galaxies.