Born at Bonn in Germany, London was the son of a mathematics professor and the younger brother of the distinguished physicist, Fritz London, with whom he collaborated on some of his early work. He was educated at the universities of Bonn, Berlin, Munich, and Breslau, where he obtained his PhD under Francis Simon in 1933. Abandoning Nazi Germany immediately afterwards, London first joined his brother at the Clarendon Laboratory in Oxford but moved to Bristol in 1936, remaining there until his brief internment as an enemy alien in 1940. On his release he worked on the separation of uranium isotopes for the development of the atomic bomb. With the coming of peace, in 1946 London joined the staff of the Atomic Energy Research Establishment at Harwell where he remained until his death.

In Oxford London continued the work of his thesis in his collaboration with his brother on a number of pressing problems in superconductivity. In particular they explained the discoveries of W. Meissner that at the moment a metal becomes superconductive it expels the magnetic field produced by an electric current; if, however, a strong external magnetic field is applied normal resistivity will return.

At Harwell after the war London worked until the 1950s on isotope separation. His attention was also drawn to the problem of superfluidity in liquid helium, which led him to develop his dilution refrigerator. This consisted in mixing the two isotopes of helium, helium-3 and helium-4, at temperatures below 1 K in a dilution of 1:1000. Some of the helium-3 would pass to and fro across the boundary between the isotopes separated by their different densities and reduce the temperature by a small amount with each passage. The machine was first described in 1951 and a working apparatus was built in 1963. The device has reached temperatures as low as 0.005 K.