Condensed Water

No , distilled water is boiled and then condensed to eliminate the impurities. Condensed water is just a matter of warm moisture in the air condensing on a cooler surface with most of the impurities still in the water.

Well, depends on how it was collected. I would imagine it would be okay, depending on how the drier makes it. Its probably evaporated, cooled on a metal plate and then collected. If you have a dehumidifier, that can be used, but id be worried about cleaning fluid residue.

Try collecting a load of it, then boil it down and see what's left behind. You probably wouldnt see anything either, but it would be a good way to eliminate its use.

In _theory_ you could. Condensed water is condensed steam. You would have to ensure there were no impurities carried over with the steam which is actually harder to do than it sounds. In actuality, there is probably lint and other particulate travelling with the steam as it exits the dryer through the common exhaust, so the condensate would have to be filtered mechanically.
Best bet is you could get a column from one of the scientific supply houses and run ordinary tap water through a resin bed which would strip it.
Here, for example is one setup (you can find cheaper systems out there):
http://www.fishersci.com/ecomm/serv...=&hasPromo=0

so sounds like the answer is technically yes...but for all practical purposes...no.

GOod luck finding distilled water in the UK. I dont know why its so hard to get a hold of.

You can make your own distillation tower. Or buy a used one for like £20 from ebay and set it up over your hob.