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Modelling robot dynamics accurately is essential for control, motion optimisation and safe human-robot collaboration. Given the complexity of modern robotic systems, dynamics modelling remains non-trivial, mostly in the presence of compliant actuators, mechanical inaccuracies, friction and sensor noise. Recent efforts have focused on utilising data-driven methods such as Gaussian processes and neural networks to overcome these challenges, as they are capable of capturing these dynamics without requiring extensive knowledge beforehand. While Gaussian processes have shown to be an effective method for learning robotic dynamics with the ability to also represent the uncertainty in the learned model through its variance, they come at a cost of cubic time complexity rather than linear, as is the case for deep neural networks. In this work, we leverage the use of deep kernel models, which combine the computational efficiency of deep learning with the non-parametric flexibility of kernel methods (Gaussian processes), with the overarching goal of realising an accurate probabilistic framework for uncertainty quantification. Through using the predicted variance, we adapt the feedback gains as more accurate models are learned, leading to low-gain control without compromising tracking accuracy. Using simulated and real data recorded from a seven degree-of-freedom robotic manipulator, we illustrate how using stochastic variational inference with deep kernel models increases compliance in the computed torque controller, and retains tracking accuracy. We empirically show how our model outperforms current state-of-the-art methods with prediction uncertainty for online inverse dynamics model learning, and solidify its adaptation and generalisation capabilities across different setups.