A search for events with a high-energy isolated electron or muon and missing transverse momentum has been performed at the electron–proton collider HERA using an integrated luminosity of 13.6 pb−1 in e−p scattering and 104.7 pb−1 in e+p scattering. Within the Standard Model such events are expected to be mainly due to W boson production with subsequent leptonic decay. In e−p interactions one event is observed in the electron channel and none in the muon channel, consistent with the expectation of the Standard Model. In the e+p data a total of 18 events are seen in the electron and muon channels compared to an expectation of 12.4±1.7 dominated by W production (9.4±1.6). Whilst the overall observed number of events is broadly in agreement with the number predicted by the Standard Model, there is an excess of events with transverse momentum of the hadronic system greater than 25 GeV with 10 events found compared to 2.9±0.5 expected. The results are used to determine the cross-section for events with an isolated electron or muon and missing transverse momentum.