Thanks Cath151 - at least that eliminates him.
Rosie17 - thanks for your interest but mother and siblings whereabouts are not useful. The children were taken into care as there mother was sent to an asylum (in Dec 1901, and she died in there), and his siblings went to different foster families in Berkshire. John was the only one taken in by family. The workhouse notes state that the uncle paid for the children's care initially but then handed them over to the workhouse once it was clear the mother was not going to recover quickly. So the Smith family took him to their home in Notts. However, the workhouse notes show 'Gone away. No address 26.1.03', so it seems they lost track of the child.
I can't find Norman Smith travelling to S Africa, but once there he ran a shop. Kate and the Smiths' own two children are on passenger lists for April 1903, so I don't know where they where for those few months between. Norman died in S Africa, and in the 1911 census Kate and her two boys are back in England.
I had thought John might have been sent to his grandmother (workhouse record shows: Ann Matthews, Baystone, Florence Rd, Chester Rd, n/t Birmingham. Widow. Lets lodgings), but the record also states she died in Dec 1902. I suppose he could have gone to her, then gone into the workhouse in Birmingham?
I have not been able to find John on passenger lists, or death records for Notts or Warks for a John Campbell around 1902/3.
Frustrating that this child seems to have evaporated!