Solution for avr-gcc Application Error with Eclipse on Windows 8.1

I'm posting this in case anybody else runs into the same problem trying to use avr-gcc from Eclipse via the AVR Plugin for Eclipse.

The problem manifests itself as avr-gcc Application Error. The application was unable to start correctly (0xc0000142) when trying to build with Eclipse. The problem seems to be that the version of GNU make included with the Arduino package is incompatible with Windows 8.1 (although earlier versions of Windows are fine). The solution is to use an alternative build of make.exe from the GNU Win32 project which seems to work fine under Windows 8.1.

The full solution, with illustrations, is posted on my blog http://smallshire.org.uk/sufficientlysmall/?p=689&preview=true.