We have carried out measurements of the pressure dependence to 1.2 GPa of the oxygen isotope effect on T(c) in the high-T(c) superconductor YBa(2)Cu(4)O(8) using a clamp cell in a superconducting quantum interference device magnetometer. This compound lies close to, but just above, the 1/8th doping point where in La(2-x)Sr(x)CuO(4) marked anomalies in isotope effects occur. Both isotopes show the same very large pressure dependence of T(c) with the result that the isotope exponent remains low (similar to 0.08), increasing slowly with pressure. This is discussed in terms of stripes, a competing pseudogap, and fluctuations.