I have never owned a tumble dryer
In our flat we had a 'pulley' as they are known in Glasgow, or a sheila maid as other people seem to call them. We had it over the bath and in a tenement with high ceilings that means you can still have baths and showers underneath it.
We also had airers in front of our radiators.
Here we have a wood burner and a clothes horse that lives beside it most of the winter.
But Green Aura is right, we hang out washing in all but the wettest of weather... right through the year. We even hang out in drizzle because it still gets dryer than it would in the house in the same amount of time. The finish it all off on the clothes horse. When we get a sunny day forecast we wash everything quickly and have stacks of wet washing ready to go out.
I know you say that you don't but if you did have a spare room to dry the washing in remember to leave the window open a crack to keep the air flowing. A dehumidifier does help but still using electricity.
I live in a VERY damp house (I mean 16 kinds of mould and rot on just about every wall, water comes in in at least 3 places when it rains) and we managed to dry right through the winter... including a wee one in re-usable nappies... so it can be done.