There is also a suggestion that it may be derived from Cockney rhyming slang in which 'sausage and mash' meant 'cash'. Hence, 'not a sausage' meant 'no money'. The phrase is not applied solely to a lack of money nowadays, though, but can refer to anything that's absent.
Q - When is a sausage not a sausage?
A - When it fails to meet EU regulations on the % of meat (otherwise it's called a phallic shaped gristle pudding or something). :o)