Dewhurst, K.A. Brunetti, E. Jaroszynski, D.A. Muratori, B.D. Owen, H.L. Wiggins, S.M. JACoW Publishing Geneva, Switzerland 978-3-95450-184-7 10.18429/JACoW-IPAC2018-TUPML021 English 1577-1580 TUPML021 Contribution to a conference proceedings 2018 2018-06 https://doi.org/10.18429/JACoW-IPAC2018-TUPML021 http://jacow.org/ipac2018/papers/tupml021.pdf The Cockcroft Beamline is to be installed at the Scottish Centre for the Application of Plasma-based Accelerators (SCAPA). The beamline is designed to transport 1 GeV electrons from a laser wakefield acceleration (LWFA) source to a pair of transverse gradient undulators. The project aims to produce X-ray undulator radiation in the first phase and free-electron laser (FEL) radiation in the second phase. The total beamline will be less than 23 m long, thus the Cockcroft Beamline has the potential to be the UK's first compact X-ray FEL. Here we present the main features of the beamline design.