A Rag, A Bone, And A Hank Of Hair — Nicholas Fisk

At the end of the 22nd century, following a nuclear accident, the birth rate is falling.

Faced with a rapidly shrinking human race, governments come up with a solution: new people from old. Cloning.

But these Reborn people are kept closely monitored, in controlled scenarios. Will they really fit into futuristic society? What other secrets are being hidden outside of the worlds in which they are contained?