A T-cell-mediated immune response is initiated by the T-cell receptor (TCR) interacting with peptide-bound major histocompatibility complex (pMHC) on an infected cell. The mechanism by which this interaction triggers intracellular phosphorylation of the TCR, which lacks a kinase domain, remains poorly understood. Here, we have introduced the TCR and associated signalling molecules into a non-immune cell and reconstituted ligand-specific signalling when these cells are conjugated with antigen-presenting cells. We show that signalling requires the differential segregation of a phosphatase and kinase in the plasma membrane. An artificial, chemically controlled receptor system generates the same effect as TCR-pMHC, demonstrating that the binding energy of an extracellular protein-protein interaction can drive the spatial segregation of membrane proteins without a transmembrane conformational change. This general mechanism may extend to other receptors that rely on extrinsic kinases, including, as we demonstrate, chimaeric antigen receptors being developed for cancer immunotherapy.