I have never had a tumble dryer and never would, they aren't necessary.
If your clothes are soaking then you need to make sure the washing machine is working right.
As someone suggested before get a dehumidifier, they are cheap and can be used all the time to reduce humidity.
Even without it my clothes only took a day to dry after washing, noy days.
I think we are all pretty much with your housemates here, why should they spend £50 on something only you want?