Child Benefit was originally Family Allowance introduced in 1946 from the Act of 1945 and was first mentioned in the Beveridge Report 1942. This report  also lead to the paying of National Insurance  contributions and the creation of the NHS.  In 1946 you would not receive any benefit for your first child, only for your second and subsequent children.  I believe this was a means of encouraging people to have more than one child, so to build up the UK population after the wars. I can not, however find anything to confirm this. It was not until 1977 that the benefit was paid for the first child.
It is evident that the intension was for this benefit to be only paid to UK citizens, as it was well before the formation of the Common Market (EU) and the Human Rights Act.
These days nobody needs encouragement to have children and therefore the time is right to amend the criteria of entitlement.  No one should be expecting the state to be responsible for their own actions.