I have a fold up bike, its one from Carrefour, called "Foldin Bike '08" You probably dont have them in the UK.
Its a great piece of kit, and I use mine to cycle about 4 miles a day across the border from Spain into Gibraltar and back to work. Which is fantastic as avoids all the frontier queues and being a bit further away I park for free every day.
It folds up - in half, and then another bolt for the handle bars to drop down. The pedals fold inwards as well. It was about 120euros.
Ive had it nearly two years now and now bits are starting to fall off, one of the chain guards, the rear mud guard is clanging around a bit. pedals get a bit sticky. But nothing a good service wouldnt fix. Its got a bit rusty too. Due to condensation formed by air conditioning in the car and being left outside of work in rainy days.
I wouldnt say its hugely sturdy. But I have ridden this bike through some pretty hurrendous weather and its held up.
Would I use it for touring? Hell no! The wheels are small and its not the easiest bike to ride at all. Even in the highest gears with a tail wind it doesnt really get much speed up. Im always being overtaken by people on full sized bikes. My journey in and out of work from the car is flat. I wouldnt even want to attempt this on some big hills. Up would be very difficult. Down would equal death, as the breaks are rubbish!
Having said that, there are other fold up bikes which are more suited to touring. My friend really likes the idea of fold up bikes but thinks mine looked silly with the smaller wheels. But he managed to find one that is practically like a mountain bike and it looks a lot more sturdy. That might be good for touring. not sure if it'd be possible to fit a rack to it. It doesnt fold up as small either.
So yeah, shop around you never know. Im sure ive read others touring on fold up bikes before.