Background The prevalence of psychological morbidity among asylum seekers and refugees is high, but these groups encounter extensive barriers to accessing health and social care. The aim of the PROSPER study was to assess the feasibility of conducting a randomised controlled trial in the UK of Problem Management Plus (PM+), an evidence-based psychosocial intervention delivered by lay therapists for distressed and functionally impaired asylum seekers and refugees. Design We undertook a feasibility study of PM+, which included a pilot study of the design features of a future definitive randomised controlled trial and economic evaluation. The feasibility study involved the adaptation of PM+ based on evidence drawn from literature synthesis and local stakeholder engagement, and a two-stage training procedure for lay therapists. These were followed by a pilot trial designed to assess the feasibility of conducting a three-arm randomised controlled trial of five 90-minute sessions of PM+, delivered individually or in groups, with 105 participants randomised 1 : 1 : 1 to individual PM+, group PM+ or a control intervention. Primary health outcomes were anxiety and depressive symptoms at 3 months; other outcomes included post-traumatic stress disorder symptoms, quality of life, progress with identified goals and service use. Findings We demonstrated that the form and content of PM+ could be adapted to meet the needs of asylum seekers and refugees. Twelve people with lived experience of the asylum process were successfully trained as lay therapists to deliver this targeted, low-intensity psychosocial intervention in local asylum seeker and refugee communities. The pilot trial was affected by governance issues. It began in December 2019 and was cut short by the COVID-19 pandemic. We were not able to complete recruitment and follow-up as planned; 11 out of 105 (10%) participants were recruited to the pilot trial (individual PM+, n = 4; group PM+, n = 3; control, n = 4); 8 out of 11 participants were followed up at 13 weeks and 7 out of 11 participants were followed up at 26 weeks. (Preliminary data were gathered on recruitment and retention, intervention fidelity and acceptability of study measures, including service use measures.) Limitations Protracted delays due to governance issues, followed by the COVID-19 pandemic, meant that we were unable to complete the pilot trial or to provide evidence regarding the feasibility of group PM+. The complexities of working with multiple languages and cultural groups were noted. There were mixed views on how successful PM+ might prove, and we had insufficient evidence to provide clear conclusions. Future work Future research could explore how technology can be used to improve the acceptability, feasibility, efficacy and potential cost-effectiveness of scalable mental health interventions and well-being support for distressed asylum seekers and refugees. The use of mobile phone and/or app-based forms of support may help to increase asylum seekers’ and refugees’ willingness to engage in research of this type. Conclusions Although it was not possible to specify the parameters for a full randomised controlled trial of PM+ for asylum seekers and refugees in the UK, our findings offer guidance on strategies that may be of value in future studies of this nature. Trial registration This trial is registered as ISRCTN15214107. Funding This project was funded by the National Institute for Health and Care Research (NIHR) Public Health Research programme and will be published in full in Public Health Research; Vol. 10, No. 10. See the NIHR Journals Library website for further project information.