The structure of a hard sphere fluid inside a planar slit pore is studied using integral equation and computer simulation approaches. A robust and efficient method of numerically solving the one-particle Ornstein-Zernike (OZ) equation for the density profile in conjunction with an arbitrary closure is described, which is an approximate Newton-Raphson iteration in Fourier space. A new form of reference hypernetted chain theory is proposed that uses the bridge function of a fluid of hard spheres near a hard wall as a reference system. This is tested against new grand canonical ensemble Monte Carlo computer simulation data obtained herein and the results of other OZ equation based theories, including the Percus-Yevick hypernetted chain, Martynov-Sarkisov and modified Verlet theory, at reduced bulk fluid number densities up to 0·7 and for pore sizes varying from 1·25 to 4·0. The proposed theory gives accurate density profiles and pressures for the entire range of slit sizes, and is superior to the other theories considered.