Accurate records of victims of modern slavery identified by various agencies allow investigators to compare different jurisdictions, track fluctuations in prevalence over time and evaluate preventative interventions. As well as enumerating those victims known to agencies, it would be desirable to know how many are working undetected under conditions of modern slavery and thus deduce the total number involved. To estimate the number of undetected potential victims of modern slavery in the UK, Bales, Hesketh and Silverman applied the method of Multiple Systems Estimation. Their approach involves fitting a statistical model to data listing victims detected by different agencies. In doing so, (a) they assume that various terms in the model are equal to 1, and (b) they only include terms not assumed to be 1 if they achieve statistical significance. In this paper, simulated datasets with known properties are used to show that if (a) is valid then (b) leads to substantial overstatement of the reliability of the estimates computed, and that if (a) is not valid then the estimation procedure is totally unsound. We conclude that Multiple Systems Estimation is not a suitable method for estimating numbers of potential victims of modern slavery.