A search for the leptonic decays of W bosons produced in the reaction e(+)p --> e(+)W(+/-)X at a centre-of-mass energy of 300 GeV has been performed with the ZEUS detector at HERA using an integrated luminosity of 47.7 pb(-1). Three events consistent with W --> e nu decay are found, giving a cross section estimate of 0.9(-0.7)(+1.0) +/- 0.2 ph, in good agreement with the Standard Model prediction. The corresponding 95% C.L. upper limit on the cross section is 3.3 pb. A search for the decay W --> mu nu has a smaller selection efficiency and yields no candidate events. Limits on the cross section for W production with large hadronic transverse momentum have been obtained. A search for high-transverse-momentum isolated tracks in events with large missing transverse momentum yields results in good agreement with Standard Model expectations, in contrast to a recent report by the H1 collaboration of the observation of an excess of such events. (C) 2000 Published by Elsevier Science B.V. All rights reserved.