Context. Remote sensing of weak and small-scale solar magnetic fields is of utmost relevance for a number of important open questions in solar physics. This requires the acquisition of spectropolarimetric data with high spatial resolution (0.1 arcsec) and low noise (1e-3 to 1e-5 of the continuum intensity). The main limitations to obtain these measurements from the ground, are the degradation of the image resolution produced by atmospheric seeing and the seeing-induced crosstalk (SIC). Aims. We introduce the prototype of the Fast Solar Polarimeter (FSP), a new ground-based, high-cadence polarimeter that tackles the above-mentioned limitations by producing data that are optimally suited for the application of post-facto image restoration, and by operating at a modulation frequency of 100 Hz to reduce SIC. Results. The pnCCD camera reaches 400 fps while keeping a high duty cycle (98.6 %) and very low noise (4.94 erms). The modulator is optimized to have high (> 80%) total polarimetric efficiency in the visible spectral range. This allows FSP to acquire 100 photon-noise-limited, full-Stokes measurements per second. We found that the seeing induced signals present in narrow-band, non-modulated, quiet-sun measurements are (a) lower than the noise (7e-5) after integrating 7.66 min, (b) lower than the noise (2.3e-4) after integrating 1.16 min and (c) slightly above the noise (4e-3) after restoring case (b) by means of a multi-object multi-frame blind deconvolution. In addition, we demonstrate that by using only narrow-band images (with low SNR of 13.9) of an active region, we can obtain one complete set of high-quality restored measurements about every 2 s.