Quote Originally Posted by lpetrich View Post
The big problem was that doing perturbation calculations resulted in awkward infinities when one tried to integrate over energies.

That problem was solved by Richard Feynman (yes, that one) and his colleagues by "renormalization" -- by noting that the infinities were always there, as it were, and could be subtracted out by redefining various quantities appropriately. This trick won him and two colleagues a Nobel Prize.
But that was after the 1930s. I guess one hot area for physicists in England in the 30s would be radar and more exactly how to generate
electromagnetic waves with a wavelength in the centimeter range rather that the meter range. Again this actually wasn't worked out until a little after the 30s. It's really kind of surprising what wasn't known in the 30s -- for example the interactions that generate energy in the Sun were not known and the pathways for generating the elements were not known.