Just to say, I think Arthur may have been born in Bromley.
As all the others I could find in the 1881 census who had the same GRO reference, 1c 680, were in Bromley St Leonard, and were born Bromley.
If so, it's a slight change from where the Mitchells were before, which might(!) explain the lack of a baptism, but not the absence of the family in the census.
John