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.