Building capable household and industrial robots requires mastering the control of versatile, high-degree-of-freedom (DoF) systems such as mobile manipulators. While reinforcement learning (RL) holds promise for autonomously acquiring robot control policies, scaling it to high-DoF embodiments remains challenging. Direct RL in the real world demands both safe exploration and high sample efficiency, which are difficult to achieve in practice. Sim-to-real RL, on the other hand, is often brittle due to the reality gap. This paper introduces SLAC, a method that renders real-world RL feasible for complex embodiments by leveraging a low-fidelity simulator to pretrain a task-agnostic latent action space. SLAC trains this latent action space via a customized unsupervised skill discovery method designed to promote temporal abstraction, disentanglement, and safety, thereby facilitating efficient downstream learning. Once a latent action space is learned, SLAC uses it as the action interface for a novel off-policy RL algorithm to autonomously learn downstream tasks through real-world interactions. We evaluate SLAC against existing methods on a suite of bimanual mobile manipulation tasks, where it achieves state-of-the-art performance. Notably, SLAC learns contact-rich whole-body tasks in under an hour of real-world interactions, without relying on any demonstrations or hand-crafted behavior priors. More information and robot videos at robo-rl.github.io