More follow up
The W Wray from the Home Children list was sent out by Middlemore Homes in 1900.
On the UK census 1901,
Albert Wray aged 6 is in the Children's Emigration Home in St Luke's Road, Birmingham. (The CEH was set up by John Middlemore, and in 1925 renamed the Middlemore Emigration Home.) The only problem is that Albert's place of birth is given as Tipton, Staffs, not Hull. However, I doubt Albert knew where he was born, so maybe the authorities were making a 'best guess'.
The records of the Home are in Birmingham Archives, and presumably access will be limited. However it should be worth contacting them to ask if this Albert is the son of Alexander and Annie. As a direct descendant, you might be able to then see his records. Just looked up the Archives, and they're moving to a new site which opens on Sept 3, so they may be slow responding to enquiries, but the general email is
library.of.birmingham@birmingham.gov.ukA possibility for
Lucy in 1901 is East Grinstead, Sussex as a Nurse Child, pob not known. 2 other nurse children in same house. Since Barnardo's practice was to place out young children in homes, this seems a strong possibility (the Home Children site says she went to Canada with a Barnardo's group)