We report measurements of branching fractions for the decays B{yields}Pl{nu}{sub l}, where P are the pseudoscalar charmless mesons {pi}{sup -}, {pi}{sup 0}, {eta} and {eta}{sup '}, based on 348 fb{sup -1} of data collected with the BABAR detector, using B{sup 0} and B{sup +} mesons found in the recoil of a second B meson decaying as B{yields}D{sup (*)}l{nu}{sub l}. Assuming isospin symmetry, we combine pionic branching fractions to obtain B(B{sup 0}{yields}{pi}{sup -}l{sup +}{nu}{sub l})=(1.54{+-}0.17{sub (stat)}{+-}0.09{sub (syst)})x10{sup -=} 4; we find 3.2{sigma} evidence of the decay B{sup +}{yields}{eta}l{sup +}{nu}{sub l} and measure its branching fraction to be (0.64{+-}0.20{sub (stat)}{+-}0.03{sub (syst)})x10{sup -4}, and determine B(B{sup +}{yields}{eta}{sup '}l{sup +}{nu}{sub l})<0.47x10{sup -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{sub ub}| in ranging from 3.6x10{sup -3} to 4.1x10{sup -3}.