The design of a Neutrino Factory (NF) has been the subject of several physics studies. For a NF based on a stored high energy muon beam, a potential key technology that has a significant impact on its cost and practicality is the ability to cool rapidly the muon beam prior to acceleration. The muon ionisation cooling experiment (MICE), currently being constructed at the Rutherford Appleton Laboratory (UK), is a demonstration of emittance cooling in a linear cooling channel. A new muon beam line and the basic infrastructure for MICE are funded, and a muon beam is under construction with an expected availability in spring 2007. The experiment will be methodically assembled over the following few years to bring the beam through RF accelerating cavities and liquid hydrogen absorbers and confined by a solenoidal magnetic field. The emittance of the beam before and after the cooling channel is measured in tracking spectrometers. The current status of the beam line and infrastructure build and of the components of MICE is presented.