Littlewood was born in Rochester in Kent, and studied at Cambridge University. Most of his work was in the field of mathematical analysis.
He collaborated for many years with G. H. Hardy, and together they devised the Hardy-Littlewood conjecture, a strong form of the twin prime conjecture.
His collaborative work, carried out by correspondence, covered fields in Diophantine approximation and Waring's problem, in particular. In his other work Littlewood collaborated with Paley in Fourier theory, and with Offord in combinatorial work on random sums, in developments that opened up fields still intensively studied. Littlewood's inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory.
He continued to write papers into his eighties, in analytical areas in what became the theory of dynamical systems, in particular.