This might be applicable, and in the correct time period -
Meanwhile, in 1850, an Act of Parliament permitted the Poor Law Guardians to
fund the emigration of any child in their care subject to permission of the Poor
Law Board. In addition, the permission of any surviving parent was to be sought
where this was possible. When this was not practicable, it was necessary to
procure the child’s agreement to his emigration, given before two justices of
the peace in a magistrates court. In 1891, the Custody of Children Act
gave the ‘rescue societies’ a legal framework within which to operate. Before
this modern child migration had operated in a grey area.

From here -



http://www.naa.gov.au/naaresources/P...g/chapter2.htm

Though it looks like the famous Liverpool Catholic didn't start sending kids abroad until 1870...

http://www.liverpoolmuseums.org.uk/m...er_nugent.aspx

Perhaps when the babies got older they were sent to Canada or Australia?