Accurate topological information is crucial in supporting the coordinated operational requirements of source-load-storage in low-voltage distribution networks. Comprehensive coverage of smart meters provides a database for low-voltage topology identification (LVTI). However, because of electricity theft, power line communication crosstalk, and interruption of communication, the measurement data may be distorted. This can seriously affect the performance of LVTI methods. Thus, this paper defines hidden errors and proposes an LVTI method based on layer-by-layer stepwise regression. In the first step, a multi-linear regression model is developed for consumer-branch connectivity identification based on the energy conservation principle. In the second step, a significance factor based on the t-test is proposed to modify the identification results by considering the hidden errors. In the third step, the regression model and significance threshold parameters are iteratively updated layer by layer to improve the recall rate of the final identification results. Finally, simulations of a test system with 63 users are carried out, and the practical application results show that the proposed method can guarantee over 90% precision under the influence of hidden errors.