The great advantage of measurement-based quantum computation is that one would simply need the ability to prepare a particular state, known as the cluster state, and subsequently to perform single-qubit measurements on it. Nevertheless, a scalable implementation is yet to be realized. Here, we propose a hybrid light–matter system consisting of coupled cavities interacting with two level systems. Utilizing the stable, individually addressable, qubits resulting from the localized long-lived atom–photon excitations, we demonstrate how to use the natural system dynamics to 'weave' these qubits into a cluster state and propose the implementation of quantum algorithms employing just two rows of qubits. Finally, we briefly discuss the prospects for experimental implementation using atoms, quantum dots or Cooper pair boxes.