During WW2 the Varsity Match was put on hold, however during those six years of global conflict Oxford and Cambridge did play each other at rugby home and away, although the results do not form part of the official Varsity Match records. The Pathe News footage in the link below, despite indicating the game was played in Dublin, was in actual fact Iffley Road in 1940.
Whilst enjoying the footage note the packed stands and how little the ground has changed in over 80 years!