My great uncle (by marriage) was born in Whitby in 1901. When he was 5 his father died. In 1911, we found him in Theydon Bois, Essex, with another boy, labelled "Home Child", with a bricklayer and his wife and their 4 children. That family later moved to Canada, and would have been glad to take him with them, but his mother declined the offer.
His younger sister was in a Home in Alverstoke, Hampshire, and his next older sister in Princess Alice Orphanage in Sutton Coldfield. We were able to get the admission documents from their successor, Action for Children. Their youngest sister was still with their mother, who couldn't afford to keep them all.
Workhouses also fostered children out, having woken up to the fact that a workhouse wasn't necessarily the best environment for children, but these are more likely to be with local people, and short term. Longer term orphans seemed to be sent anywhere, to any Children's Home that would take them.
