Twickenham railway station was in the course of being resited during the late-1930s. The original station was west of the old road bridge and the new one east of it. The skeleton of the new platforms and much of the associated track work was already in place when the scheme was halted by the outbreak of WWII. After the war, some work was done on the platforms to enable them to be used, hand-signalled, for rugby event traffic, but the completion of the new station was slowed by the post-war shortages of materials and money. It eventually came into use in March 1954, the old station being quickly demolished, finally the road bridge was rebuilt shortly after the demise of the trolleybuses crossing it in May 1962 - it was held together by the tram tracks surviving in the road surface!
The new East box of 1938 was almost certainly commissioned as part of the stage works for this scheme, but circumstances demanded that it remained in use far longer than had been originally intended. The signalling in this area had been, and remained, "interesting" because of the special arrangements to cope with rugby traffic.
Blast damage in August 1944 would almost certainly have been from an exploding V1 "doodlebug", around 100 a day were being targetted on London at this period and obviously a fair proportion of these caused some damage to railway property.