We present Multi-Element Radio-Linked Interferometer Network (MERLIN) observations of OH maser and radio continuum emission within a few hundred pc of the core of the ultraluminous infrared galaxy (ULIRG) Markarian 231. This is the only known OH megamaser galaxy classed as a Seyfert 1. Maser emission is identified with the 1665- and 1667-MHz transitions over a velocity extent of 720 km s-1. Both lines show a similar position-velocity structure including a gradient of 1.7 km s-1 pc-1 from NW to SE along the 420-pc major axis. The (unresolved) inner few tens of pc possess a much steeper velocity gradient. The maser distribution is modelled as a torus rotating about an axis inclined at ~45° to the plane of the sky. We estimate the enclosed mass density to be 320 +/- 90Msolarpc-3 in a flattened distribution. This includes a central unresolved mass of <~8 × 106Msolar. All the maser emission is projected against a region with a radio continuum brightness temperature >=105 K, giving a maser gain of <=2.2. The 1667:1665 MHz line ratio is close to 1.8 (the value predicted for thermal emission) consistent with radiatively pumped, unsaturated masers. This behaviour and the kinematics of the torus suggest that the size of individual masing regions is in the range 0.25-4 pc with a covering factor close to unity. There are no very bright compact masers, in contrast to galaxies such as the Seyfert 2 Markarian 273, where the masing torus is viewed nearer edge-on. The comparatively modest maser amplification seen from Markarian 231 is consistent with its classification in the unification scheme for Seyfert galaxies. Most of the radio continuum emission on 50-500 pc scales is probably of starburst origin but the compact peak is 0.4 per cent polarized by a magnetic field running north-south, similar to the jet direction on these scales. There is no close correlation between maser and continuum intensity, suggesting that much of the radio continuum must originate in the foreground and indeed the relative continuum brightness is slightly greater in the direction of the approaching jet. Comparisons with other data show that the jet changes direction close the nucleus and suggest that the sub-kpc disc hosting the masers and starburst activity is severely warped.