Fairness in machine learning is more important than ever as ethical concerns continue to grow. Individual fairness demands that individuals differing only in sensitive attributes receive the same outcomes. However, commonly used machine learning algorithms often fail to achieve such fairness. To improve individual fairness, various training methods have been developed, such as incorporating fairness constraints as optimisation objectives. While these methods have demonstrated empirical effectiveness, they lack formal guarantees of fairness. Existing approaches that aim to provide fairness guarantees primarily rely on verification techniques, which can sometimes fail to produce definitive results. Moreover, verification alone does not actively enhance individual fairness during training. To address this limitation, we propose a novel framework that formally guarantees individual fairness throughout training. Our approach consists of two parts, i.e., (1) provably fair initialisation that ensures the model starts in a fair state, and (2) a fairness-preserving training algorithm that maintains fairness as the model learns. A key element of our method is the use of randomised response mechanisms, which protect sensitive attributes while maintaining fairness guarantees. We formally prove that this mechanism sustains individual fairness throughout the training process. Experimental evaluations confirm that our approach is effective, \emph{i.e.}, producing models that are empirically fair and accurate. Furthermore, our approach is much more efficient than the alternative approach based on certified training (which requires neural network verification during training).