Quantum phase transition achieved by fine tuning the continuous phase transition down to zero kelvin is a challenge for solid state science. Critical phenomena distinct from the effects of thermal fluctuations can materialize when the electronic, structural or magnetic long-range order is perturbed by quantum fluctuations between degenerate ground states. Here we have developed chemically pure tetrahalo-p-benzoquinones of n iodine and 4-n bromine substituents (QBr4-nIn, n=0-4) to search for ferroelectric charge-transfer complexes with tetrathiafulvalene (TTF). Among them, TTF-QBr2I2 exhibits a ferroelectric neutral-ionic phase transition, which is continuously controlled over a wide temperature range from near-zero kelvin to room temperature under hydrostatic pressure. Quantum critical behaviour is accompanied by a much larger permittivity than those of other neutral-ionic transition compounds, such as well-known ferroelectric complex of TTF-QCl4 and quantum antiferroelectric of dimethyl-TTF-QBr4. By contrast, TTF-QBr3I complex, another member of this compound family, shows complete suppression of the ferroelectric spin-Peierls-type phase transition.