I actually have a little 125cc bike sitting in the garage unused (anyone want to buy it?).
For sure I'm dismissing most of the proposals here and the reason for this is that I believe when you work out the total cost of running a car for commuting it is a very complicated thing to work out.
If I am to establish the cheapest means possible whilst also trying to mitigate or reduce where possible the potentially expensive costs of mechanical failure it gets even harder to work out.
In terms of a second hand Smart car (which was my first thought), I would have to factor in the fact that Smart cars have very common engine problems and I would almost certainly have to factor in an engine rebuild or even rebuilds into the overall running costs.
Fuel consumption is probably the biggest single cost therefore in my circumstances, a £50 car that does 25mpg will be a more expensive solution than a £2000 car that does 50mpg even if both cars have zero worth after 12 months.
Cheap road tax, cheap insurance all help but they are by no means a priority compared to the other costs.
There must some way of calculating be a mathematical equation to combine all the running costs, the odds of costly mechanical failure and the depreciation. If only I knew what it was?
In the immediate term I'm going to try and find out why my 1200 bandit only gets 26mpg. If I can solve that, it takes the immediate requirement away but once the frosts set in, I want the combination of a roof and a heater and 40mpg which probably means BlackC555's Diesel Fiesta suggestion is the closest so far. Perhaps a Skoda Fabia Diesel even - plenty of them for less than a grand.