Cognitive remediation (CR) training has emerged as a promising approach to improving cognitive deficits in schizophrenia and related psychosis. The limited availability of psychological services for psychosis is a major barrier to accessing this intervention however. This study investigated the effectiveness of a low support, remotely accessible, computerised working memory (WM) training programme in patients with psychosis. Ninety patients were enrolled into a single blind randomised controlled trial of CR. Effectiveness of the intervention was assessed in terms of neuropsychological performance, social and occupational function, and functional MRI 2 weeks post-intervention, with neuropsychological and social function again assessed 3-6 months post-treatment. Patients who completed the intervention showed significant gains in both neuropsychological function (measured using both untrained WM and episodic task performance, and a measure of performance IQ), and social function at both 2-week follow-up and 3-6-month follow-up timepoints. Furthermore, patients who completed MRI scanning showed improved resting state functional connectivity relative to patients in the placebo condition. CR training has already been shown to improve cognitive and social function in patient with psychosis. This study demonstrates that, at least for some chronic but stable outpatients, a low support treatment was associated with gains that were comparable with those reported for CR delivered entirely on a 1:1 basis. We conclude that CR has potential to be delivered even in services in which psychological supports for patients with psychosis are limited.