Ultra-thin magnetic dielectric films are of prime importance due to their applications for nanophotonics and spintronics. Here, we propose an efficient method for the magneto-optical investigation of ultra-thin magnetic films which allows one to access their state of magnetization and magneto-optical properties. It is based on the surface-plasmon-polariton-assisted transverse magneto-optical Kerr effect (TMOKE). In our experiments, sub-100 nm-thick bismuth-substituted lutetium iron-garnet films covered with a plasmonic gold grating have been analyzed. The excitation of surface plasmon-polaritons provides resonance enhancement of TMOKE up to 0.04 and makes it easily detectable in the experiment. For films thicker than 40 nm, the TMOKE marginally depends on the film thickness. A further decrease in the film thickness diminishes TMOKE since for such thicknesses the surface plasmon-polariton field partly penetrates inside the non-magnetic substrate. Nevertheless, the TMOKE remains measurable even for few-nm-thick films, which makes this technique unique for the magneto-optical study of ultra-thin films. Particularly, the proposed method reveals that the off-diagonal components of the magnetic film permittivity tensor grow slightly with the reduction of the film thickness.