Regaining hand and arm function is an important step towards regaining independence following high-level spinal cord injury (tetraplegia). The delivery of small electrical pulses over the skin above the spinal cord, called transcutaneous spinal cord stimulation (tESCS), appears to improve the arm and hand function of people who have had tetraplegia for several years when delivered at the same time as upper limb therapy. However, tESCS has not been tested in people who have a new spinal cord injury. It should be straightforward to deliver tESCS during standard upper limb therapy sessions to inpatients receiving primary rehabilitation. The investigators want to test the practical aspects of delivering this intervention and also to compare recovery between a group of people who only receive upper limb therapy and a group who receive upper limb therapy and tESCS. If successful, tESCS could in the future be used as part of regular therapy following an acute spinal cord injury. Benefits could include faster and better recovery, reduced stay in hospital, and reduced NHS costs.