It is proposed to install a Muon Ionisation Cooling Experiment (MICE) at the ISIS facility, at Rutherford Appleton Laboratory (RAL). This experiment will be the first demonstration of ionisation cooling as a means to reduce the large transverse emittance of the muon beam produced during the early stages of a Neutrino Factory. In order to permit a realistic demonstration of cooling, a beam of muons must be produced, possessing particular qualities, notably in emittance and momenta. This paper describes the current design for the muon beamline, outlining issues particular to the needs of the MICE experiment, and discusses its expected performance.