<p>Whilst refactoring some old code I realised that a particular header file was full of function declarations for functions long since removed from the .cpp file.  Does anyone know of a tool that could find (and strip) these automatically?</p>

If you index to code with Doxygen you can see from where is each function referenced. However, you would have to browse through each class (1 HTML page per class) and scan for those that don't have anything pointing to them.
Alternatively, you could use ctags to generate list of all functions in the code, and then use objdump or some similar tool to get list of all function in .o files - and then compare those lists. However, this can be problematic due to name mangling.