A search for events with a high energy isolated lepton 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 101.6 pb^-1 in e^+ p scattering. Within the Standard Model such events are expected to be due to W boson production, with subsequent leptonic decay. The analysis has been tuned to maximise the acceptance of such events, and reject other Standard Model processes. In e^- p interactions no events are observed, consistent with the expectation of the Standard Model in this low luminosity sample. In the e^+ p data 18 events are seen in the electron and muon channel compared to an expectation of 10.5 +-2.5 dominated by W production (8.2 +-2.5). The excess above the expectation is mainly due to events with transverse momentum of the hadronic system greater than 25 GeV where 10 events are found compared to 2.8 +-0.7 expected.