Observations are presented of high resolution interstellar Na I D and K I (lambda 7699 Angstroms) line profiles towards 7 stars in the globular cluster NGC 6541 and 3 field stars within 3° of the cluster. It is seen that the gas in this general direction (l, b ~ 350°, -11°) shows a complex structure, having the greatest number of components yet identified in one of our cluster sightlines, with absorption components detected over an LSR velocity range ~ -100 to +100 km s(-1) . We consider, as far as possible, the identification of the observed gas components. In the low-velocity gas we identify the extensive and nearby diffuse gas which contains the cold, dark and molecular clouds observed closer to the Galactic plane. Components are tentatively identified with both positive and negative peculiar velocity gas components produced by outlying gas in the Sagittarius arm, with gas in the Scutum-Crux and the 3 kpc arms, with an H I filament detected in radio mapping and with shell-like structures expanding from the Sco-Cen association. From the cluster star spectra some variability in the fine scale gas structure is seen on a scale of a few arcsecs.