If you literally want the cheapest new car you can get to run for £6k, get a 1.2 (petrol) Fiat Panda. It's white goods, it's not unpleasant to drive, does loads to the gallon, uses bugger all fuel, costs something like £15 to tax it and all round is just good at being cheap and reliable. Diesel as a rule is not as economical in the long run on these very small cars with little engines.
Personally I went down the route of buying a much older, more comfortable car for half that about 5 years ago (£3k buys an awful lot of fuel) for commuting. Does about 35mpg as opposed to 50 odd or what ever it is the Panda does. £225 tax, but classic insurance so that's nothing. Servicing costs me around £30 a pop as it's a doddle to service and parts cost bugger all for it (I swapped all the disks and pads for £80).
To be fair I have spent a grand this year getting it resprayed as the original paint wasn't clearcoated and it'd gone blotchy over the years. But the theory there is that it should last at least another 20 years and look great. Certainly as I plan to run this car until it's death (it's done 70k miles now, they're good for at least 200k if you look after them right).
Two different options depending on how you see cars.
