Context. The link between how bipolar planetary nebulae are shaped and their central stars is still poorly understood. Aims: This paper investigates the kinematics and shaping of the multipolar nebula M 1-75, and briefly discusses the location and nature of its central star. Methods: Fabry-Perot data from GHαFAS on the WHT that samples the Doppler shift of the [Nii] 658.3 nm line are used to study the dynamics of the nebula by means of a detailed 3D spatio-kinematical model. Multi-wavelength images and spectra from the WFC and IDS on the INT, as well as from ACAM on the WHT, allowed us to constrain the parameters of the central star. Results: The two pairs of lobes, angularly separated by ~22°, were ejected simultaneously approx. ~3500-5000 years ago, at the adopted distance range from 3.5 to 5.0 kpc. The larger lobes show a slight degree of point symmetry. The formation of the nebula could be explained by wind interaction in a system consisting of a post-AGB star surrounded by a disc warped by radiative instabilities. This requires the system to be a close binary or a single star that engulfed a planet as it died. On the other hand, we present broad- and narrow-band images and a low S/N optical spectrum of the highly-reddened, previously unnoticed star that is likely the nebular progenitor. Its estimated V-I colour allows us to derive a rough estimate of the parameters and nature of the central star. Based on observations made with the 4.2 m William Herschel Telescope and the 2.5 m Isaac Newton Telescope, both operated on the island of la Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.