Agreed ... unrelated, maybe, but surely there would not have been more than one Margaret M Walker in the village at the time of Clement's death, so she must be the one the OP is looking for.
Married 1931, so the local person would be Margaret Mary Skinner born Wellingborough Dec 1909 to George & Mary living in Wellingborough.
At least a dozen Arthur Walkers born locally at similar time.
Neither seem to appear on the 1939 reg, pity. Seems an odd time, 1942, for a youngish man to be taking over a pub ... I wonder what Arthur's circumstances were.