The impact of pressure on the hydrodynamic instability mechanism is investigated in weakly turbulent, lean methane-air premixed slot flames by means of direct numerical simulations (DNS) employing multi-step chemistry and two different species diffusion models. A dedicated set of slot flames at four different pressures, featuring the same hydrodynamic lengthscale in units of flame thickness, is designed such that the Darrieus-Landau instability mechanism is either suppressed or present in the different flames. For the DNS design, a linear stability analysis is conducted to determine the flame stability characteristics and in particular the cutoff length scale of the Darrieus-Landau instability. As the pressure increases, the cutoff length scale decreases significantly in both dimensional and nondimensional units using the flame thickness as a reference. As a result, an increase in pressure promotes the onset and persistence of the Darrieus-Landau (or hydrodynamic) instability in the slot flame configuration considered. The impact of pressure is investigated in terms of flame morphology using well-established hydrodynamic instability markers. Then, the effect of pressure on the flame speed enhancement caused by the instability is assessed and quantified resorting to the global consumption speed concept. In particular, it is found that over the entire flame brush, the curvature skewness is more negative as pressure increases from 1 to 8 atm and the flame speed is increased by a factor that spans from 1.9 to 1.15 trough the flame brush.