Accurate localisation is a critical component in modern wireless communication systems, especially in complex environments with a very low signal-to-noise ratio (SNR). Reconfigurable intelligent surfaces (RIS) have emerged as a promising solution to enhance localisation accuracy by dynamically controlling signal reflection patterns. Motivated by the need for precise localisation solutions, this study introduces the RIS-enhanced hybrid localisation network (RHL-Net), a novel framework that integrates RIS with advanced deep learning techniques. RHL-Net employs long short-term memory (LSTM) networks for temporal data processing and Kolmogorov-Arnold networks (KAN) for spatial feature extraction. The key innovation of using KAN lies in its superior ability to learn complex spatial structures compared to traditional Multi-Layer Perceptrons (MLPs); KANs achieve higher accuracy with significantly fewer parameters and offer greater interpretability through their spline-based activation functions, which are learnable and adaptable. This makes KAN uniquely suited for distilling the intricate spatial fingerprints from the RIS-enhanced channel for precise location estimation. For performance evaluation, RHL-Net uses a dataset acquired from a dual-channel universal software radio peripheral (USRP) system, which records received signal strength (RSS) and channel phase response within a single-input multiple-output (SIMO) orthogonal frequency division multiplexing (OFDM) system. A dual-channel USRP with two antennas at the receiver ( ) side is deployed at a grid of positions with an interspacing distance ( ) to assess the RHL-Net localisation performance. Experimental results show that for metres with Directive and Monopole antenna configurations, RHL-Net achieves average accuracies of and , respectively, with RIS activated, significantly outperforming the deactivated configuration. Similarly, for metre, Directive and Monopole setups achieve average accuracies of and , respectively, with RIS activation. These results demonstrate the effectiveness of RHL-Net in harnessing RIS technology and the advanced spatial modeling of KAN for precise localisation, outperforming state-of-the-art methods on the evaluated dataset.