Inference of the causal structure that induces correlations between two traits can be achieved by combining genetic associations with a mediation-based approach, as is done in the causal inference test (CIT) and others. However, we show that measurement error in the phenotypes can lead to mediation-based approaches inferring the wrong causal direction, and that increasing sample sizes has the adverse effect of increasing confidence in the wrong answer. Here we introduce an extension to Mendelian randomisation, a method that uses genetic associations in an instrumentation framework, that enables inference of the causal direction between traits, with some advantages. First, it is less susceptible to bias in the presence of measurement error; second, it is more statistically efficient; third, it can be performed using only summary level data from genome-wide association studies; and fourth, its sensitivity to measurement error can be evaluated. We apply the method to infer the causal direction between DNA methylation and gene expression levels. Our results demonstrate that, in general, DNA methylation is more likely to be the causal factor, but this result is highly susceptible to bias induced by systematic differences in measurement error between the platforms. We emphasise that, where possible, implementing MR and appropriate sensitivity analyses alongside other approaches such as CIT is important to triangulate reliable conclusions about causality.