Background: Routine HIV pre-exposure prophylaxis (PrEP) and HIV care appointments provide opportunities for screening men who have sex with men (MSM) for hepatitis C virus infection (HCV). However, levels of screening required for achieving the WHO elimination target of reducing HCV incidence by 90% by 2030 among all MSM are unknown. Methods: An HCV/HIV transmission model was calibrated to UK prevalence of HIV among MSM (4·7%) and chronic HCV infection among HIV-positive MSM (9·9%) and HIV-negative MSM (1.2%). Assuming 12·5% coverage of PrEP among HIV-negative MSM, we evaluated the relative reduction in overall HCV incidence by 2030 (compared to 2018 levels) of HCV screening every 12/6-months (alongside completing direct acting antiviral treatment within 6-months of diagnosis) in PrEP users and/or HIV-diagnosed MSM. We estimated the additional screening required among HIV-negative non-PrEP users to reduce overall incidence by 90% by 2030. The effect of 50% reduction in condom use among PrEP users (risk compensation) was estimated. Results: Screening and treating PrEP users for HCV every 12 or 6-months decreases HCV incidence by 67·3% (uncertainty range 52·7–79·2%) or 70·2% (57·1–80·8%), respectively, increasing to 75·4% (59·0–88·6%) or 78·8% (63·9–90·4%) if HIV-diagnosed MSM are also screened at same frequencies. Risk compensation reduces these latter projections by <10%. To reduce HCV incidence by 90% by 2030 without risk compensation, HIV-negative non-PrEP users require screening every 5·6 (3·8–9·2) years if MSM on PrEP and HIV-diagnosed MSM are screened every 6-months, shortening to 4·4 (3·1–6·6) years with risk compensation. For 25·0% PrEP coverage, the HCV elimination target can be reached without screening HIV-negative MSM not on PrEP, irrespective of risk compensation. Interpretation: At low PrEP coverage, increased screening of all MSM is required to achieve the WHO HCV-elimination targets for MSM in the UK, whereas at higher PrEP coverage this is possible through just screening HIV-diagnosed MSM and PrEP users. Keywords: Pre-exposure prophylaxis, Hepatitis C virus, HIV, Men who have sex with men, Antiviral treatment, Prevention, Risk compensation