Context. The Lyman alpha emission line of neutral hydrogen is an important tool for finding galaxies at high redshift, thus for probing the structure of the early universe. However, the resonance nature of the line and its sensitivity to dust and neutral gas is still not fully understood.Aims. We present measurements of the velocity, covering fraction and optical depth of neutral gas in front of two well-known, local blue compact galaxies that show Lyman alpha in emission: ESO 338-IG 04 and Haro 11. We thus observationally test the hypothesis that Lyman alpha can escape through neutral gas by being Doppler shifted out of resonance. Methods. We present integral field spectroscopy, obtained with the GIRAFFE/Argus spectrograph at VLT/FLAMES in Paranal, Chile. The excellent wavelength resolution allowed us to accurately measure the velocity of the ionized and neutral gas through the Hα emission and Na D absorption, which trace the ionized medium and cold interstellar gas, respectively. We also present independent measurements from the VLT/X-shooter spectrograph that confirm our results. Results. For ESO 338-IG04 we measure no significant shift of neutral gas: the best fit velocity offset is −15 ± 16 km s −1 . For Haro 11, we see an outflow from knot B at 44 ± 13 km s −1 , and infalling gas towards knot C with 32 ± 12 km s −1 . Based on the relative strength of the Na D absorption lines, we estimate low covering fractions of neutral gas (down to 10%) in all three cases. Conclusions. The Na D absorption most likely occurs in dense clumps with higher column densities than the medium in which the bulk of the Ly α scattering takes place. Still, we find no strong correlation between outflowing neutral gas and strong Ly α emission. The Ly α photons from these two galaxies are therefore likely to be escaping due to a low column density and/or covering fraction.