We can't hang our clothes out to dry, so in fall and spring when it's too warm to use our heat but not hot enough for the clothes to dry quickly naturally, they also used to get stiff and have a musty, fausty smell to them. I tried changing the detergent, cleaning the machine, and always laying out the laundry as soon as the washing cycle finished, but it still smelled.
We ended up getting the heated tower airer from Lakeland because we didn't have space or money for a tumble dryer, and we love it. The clothes always dry in less than 24 hours, and I think the long drying time before was what was causing the smell. It fits a whole load of wash on it so it's also great knowing I can do a load of laundry every day if I need to, because I don't need to wait 2-3 days for it to dry anymore. It plugs into an electrical socket so the actual rungs of the airer are heated, and that costs around 3p per hour to run. It's around £80 and for some reason I've only ever seen them sold at Lakeland and an ad in a small local newspaper, but it's seriously amazing. Two other women at work were also having trouble with fausty smelling clothes, especially the collars of polo shirts, so they bought the airer too on my recommendation. They can both dry outside so only use theirs when the weather's bad, but they're happy with them, and I use mine all the time and it's lovely.