Alasdair Taylor's Answer

The short answer is no.

The long answer is this:

If a document is protected by copyright, then under the Copyright Designs and Patents Act 1988 the copying of a “substantial part” of that document without the permission of the copyright owner will constitute copyright infringement.  It is immaterial whether additional material has been added to the document – whether a derivative work has been created. 

Even if you have added so much material that only a small fraction of the derivative work comes from the original document, then copying will still infringe the copyright.  In other words, the question is whether a substantial part of the original work is copied, not whether the original work forms a substantial part of the derivative work. 

In this context, I should also mention that substantiality is assessed in a qualitative as well as a quantative manner, so even a relatively small part of a work (e.g. a few lines from a poem) may be substantial.