In power distribution networks, the correct identification of network topology and parameters is critical in maintaining efficient operating conditions. Operative efficiency and reliability are major goals in such networks. Satisfying these conditions necessitates a clear understanding of network parameters and topology, particularly in low-voltage power distribution networks, which are typically characterized by complicated patterns and fluctuating load demands. This research presents a novel approach utilizing the Voltage Regulator Weighted Topology Recurrent Neural Network (VRWT-RNN) for joint identification of parameters and topology in low-voltage distribution networks. The Low-Voltage Network Dataset is used to capture time-series data from five nodes in a low-voltage electrical distribution network, and Z-score normalization was used for data preprocessing. The VR-WT-RNN approach combines weighted topology considerations within a recurrent neural network structure, enhancing its ability to accurately model and predict sophisticated network behaviors. Using records of voltage regulator settings, load profiles, and network configurations, the model can predict both network parameters and topology. The performance of the VR-WT-RNN model shows an effectiveness of up to 5% accuracy improvement for Transformer 2, accompanied by significant gains in NMI and ARI over traditional methods. Further, the responsiveness of the model towards dynamic variations of network conditions marks its usability within changing operating conditions.