High pressure was used to investigate the stability of the non-Fermi liquid (NFL) state, observed in electrical resistivity of uranium-based band metamagnet UCoAl in a pure form (paramagnet) or with Fe substitution (ferromagnetic ground state), both in a single-crystal form. By combining the pressure variations of magnetization and resitivity in these materials the phase diagram for UCoAl had been constructed. The band metamagnet transforms into the ferromagnetic state as the critical metamagnetic field is reduced to zero by the lattice expansion analogous to the negative pressure. Within the same diagram, the increasing hydrostatic pressure drives the critical metamagnetic field upwards while reducing the magnetization increment at the transition. The NFL state persists to about 4-5 GPa. Although spin fluctuations play an important role in the character of UCoAl, they do not exhibit any criticality in the sense of divergence of parameters describing the resistivity around the Ferro-NFL phase transition, which is of the first order type.