Modelling suggests hepatitis C virus (HCV) elimination is possible among men who have sex with men (MSM), with key screening groups including HIV‐diagnosed MSM and MSM using pre‐exposure prophylaxis (PrEP). Mathematical modelling was used to determine the cost‐effectiveness of HCV case‐finding strategies among MSM from the provider perspective, and to determine which interventions could achieve a 90% reduction in HCV incidence over 2015–2030. At baseline, we assumed symptomatic screening in HIV‐negative MSM (including PrEP users) and 12‐monthly screening among HIV‐diagnosed MSM. Improved case‐finding strategies included screening alongside HIV testing in HIV‐negative MSM not using PrEP (PrEP non‐users); 12/6/3‐monthly screening in PrEP users; and 6‐monthly screening in HIV‐diagnosed MSM, with the cost‐effectiveness being compared incrementally. Costs (GBP) and quality‐adjusted life years (QALYs) were assessed to estimate the mean incremental cost‐effectiveness ratio (ICER) with a time horizon to 2050, compared to a willingness‐to‐pay threshold of £20,000/QALY. From the baseline, the most incrementally cost‐effective strategy is to firstly undertake: (1) 12‐monthly HCV screening of PrEP users (gaining 6715 QALYs with ICER £1760/QALY), followed by (2) HCV screening among PrEP non‐users alongside HIV testing (gaining 7048 QALYs with ICER £4972/QALY). Compared to the baseline, this combined strategy would cost £46.9 (95%CrI £25.3–£66.9) million and achieve the HCV elimination target in 100% of model runs. Additional screening incurs ICERs >£20,000/QALY compared to this combined strategy. In conclusion, HCV elimination can be achieved cost‐effectively among UK MSM. Policymakers should consider scaling‐up HCV screening in HIV‐negative MSM, especially PrEP users, for achieving this target.