Treatment as Prevention (TasP) using directly-acting antivirals has been advocated for Hepatitis C Virus (HCV) in people who inject drugs (PWID), but treatment is expensive and TasP's effectiveness is uncertain. Previous modelling has assumed a homogeneously-mixed population or a static network lacking turnover in the population and injecting partnerships. We developed a transmission-dynamic model on a dynamic network of injecting partnerships using data from survey of injecting behaviour carried out in London, UK. We studied transmission on a novel exponential-clustered network, as well as on two simpler networks for comparison, an exponential unclustered and a random network, and found that TasP's effectiveness differs markedly. With respect to an exponential-clustered network, the random network (and homogeneously-mixed population) overestimate TasP's effectiveness, whereas the exponential-unclustered network underestimates it. For all network types TasP's effectiveness depends on whether treated patients change risk behaviour, and on treatment coverage: higher coverage requires fewer total treatments for the same health gain. Whilst TasP can greatly reduce HCV prevalence, incidence of infection, and incidence of reinfection in PWID, assessment of TasP's effectiveness needs to take account of the injecting-partnership network structure and post-treatment behaviour change, and further empirical study is required.