Just spotted this old thread and thought I'd add my experience. We built an extension last year and included a small 5 ft squared 'drying room'. They have them in fire stations for drying wet gear. It is a windowless room, with a small dehumidifier (approx. 70 euro from argos), that is very quiet. It has overhead rails for sheets etc. and two tower clothes horses. It fits about three loads of washing at one time and dries them in about six/eight hours.
The clothes are soft, require little ironing and the fibres aren't damaged like a tumble dryer tends to do. Best of all, our electricity bill is down 100 euro from the same time last year despite the new extension. The tumble dryer is redundant along with its noisy hum and high running costs.
There is a radiator in the room, which adds heat in the evening and may speed up the drying time, but this is not essential as clothes just need dry air - be that cold or warm.
The builder suggested fitting a fan in the room, although I thought this unnecessary. I have used it with the dehumidifier. However it made no difference to the speed of drying and it was using electricity, so I don't use it now.
A specific room like this is not essential as the same principals could be used in any spare corner.