We report measurements of branching fractions for the decays B-->Plnu_{l}, where P are the pseudoscalar charmless mesons pi;{-}, pi;{0}, eta and eta;{'}, based on 348 fb;{-1} of data collected with the BABAR detector, using B0 and B+ mesons found in the recoil of a second B meson decaying as B-->D;{(*)}lnu_{l}. Assuming isospin symmetry, we combine pionic branching fractions to obtain B(B;{0}-->pi;{-}l;{+}nu_{l})=(1.54+/-0.17_{(stat)}+/-0.09_{(syst)})x10;{-4}; we find 3.2sigma evidence of the decay B;{+}-->etal;{+}nu_{l} and measure its branching fraction to be (0.64+/-0.20_{(stat)}+/-0.03_{(syst)})x10;{-4}, and determine B(B;{+}-->eta;{'}l;{+}nu_{l})<0.47x10;{-4} to 90% confidence level. Using partial branching fractions for the pionic decays in ranges of the momentum transfer and a variety of form factor calculation, we obtain values of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |V_{ub}| in ranging from 3.6x10;{-3} to 4.1x10;{-3}.