The Hollow Men

You may be looking for the novel, The Hollow Men.

The Hollow Men was a poem by T.S. Eliot.

Barbara Wright quoted the line "This is the way the world ends, not with a bang but a whimper." (ST: 1963)

Richard Lazarus quoted the poem to Tish Jones in saying "Between the idea, and the reality, between the motion, and the act..." With the Doctor finishing "...falls the shadow".

After Lazarus' death, the Doctor told Martha Jones that Eliot was right, quoting "This is the way the world ends, not with a bang but a whimper". (DW: The Lazarus Experiment)