When your rear gear cable snaps, the derailleur mechanism forces the arm to the smallest and highest cog, making it a hard work ride home. Some people have mentioned tugging hard on the loose cable and tying it off on the bike somehow. Courtesy of Simon, there is a simpler alternative. The answer is a pebble or piece of twig with a thickness of around 10mm.
You need to pull the derailleur arm back and towards the wheel to open up the "derailleur parallelogram" (splendid description Simon) and insert the spacer. That should enable you to have a fixed gear that is somewhat larger and lower than the smallest to continue your trip. It certainly worked for me on Wednesday. Glad I was in knowledgeable company. I was even allowed to take a shortcut to the pub missing a pre-lunch hilly loop, where I recorded the pebble for posterity.
This temporary fix is not perfect, as the chain will not be perfectly aligned / indexed with the cassette (unless you are very lucky with your chosen pebble) so expect some squeaks and accelerated wear and tear to chain and cassette.
The real Fixie Dave does not suffer this type of problem!