Jean,
If he is the one registered Dec 1881, then the 1881 census is going to be pretty close to his conception. I had a look through Greenwich, Eltham, Chislehurst and Bromley for Whiting/Marshall connections and could only find one extremely speculative possibility, with no apparent connection to the Barrs. I'm not even going to embarrass myself by posting it. I'll wait until you get the birth certificate.
Phil