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Objective Universal Basic Income (UBI)—a largely unconditional, regular payment to all adults to support basic needs—has been proposed as a policy to increase the size and security of household incomes and promote mental health. We aimed to quantify its long-term impact on mental health among young people in England.Methods We produced a discrete-time dynamic stochastic microsimulation that models a close-to-reality open cohort of synthetic individuals (2010–2030) based on data from Office for National Statistics and Understanding Society. Three UBI scheme scenarios were simulated: Scheme 1—Starter (per week): £41 per child; £63 per adult over 18 and under 65; £190 per adult aged 65+; Scheme 2—Intermediate (per week): £63 per child; £145 per adult under 65; £190 per adult aged 65+; Scheme 3—Minimum Income Standard level (per week): £95 per child; £230 per adult under 65; £230 per adult aged 65+. We reported cases of anxiety and depression prevented or postponed and cost savings. Estimates are rounded to the second significant digit.Results Scheme 1 could prevent or postpone 200 000 (95% uncertainty interval: 180 000 to 210 000) cases of anxiety and depression from 2010 to 2030. This would increase to 420 000(400 000 to 440 000) for Scheme 2 and 550 000(520 000 to 570 000) for Scheme 3. Assuming that 50% of the cases are diagnosed and treated, Scheme 1 could save £330 million (£280 million to £390 million) to National Health Service (NHS) and personal social services (PSS), over the same period, with Scheme 2 (£710 million (£640 million to £790 million)) or Scheme 3 (£930 million (£850 million to £1000 million)) producing more considerable savings. Overall, total cost savings (including NHS, PSS and patients’ related costs) would range from £1.5 billion (£1.2 billion to £1.8 billion) for Scheme 1 to £4.2 billion (£3.7 billion to £4.6 billion) for Scheme 3.Conclusion Our modelling suggests that UBI could substantially benefit young people’s mental health, producing substantial health-related cost savings.