We're in eastern Victoria and have similar issues - the hills hoist is in full sun, on a hill, lots of sun but stuff only comes in mostly dry after a full day out in winter, even the sunny ones like today. The heavy dew means nothing can be left out overnight and the grass is wet till around 10am, not the best for evaporation!
My plan is a 2 or 3 sided room/shed with polycarbonate roofing, something like 2.8 x 3.5m, longer side facing north, walls on the south and west, where the rain comes from, but ideally a few windows in there too for more breeze. We get sideways rain up to 6 feet high on the back verandah door even with the roof over it so no wall isn't an option.
I want to go a bit fancy and have a roof high enough that raising the clothes with a winch leaves me a useable work space for also drying herbs and dyeing and so on. Plus flyscreens on the north side. Standard shed roof tilted north, decent angle, gutter on the south and tank behind. Option then for hand washing clothes and fleece in my little workspace.
Easy cheap option is a cover on a hills hoist, but that means buying one to start with, since it sounds like you don't have one. But a simple 4 posts and polycarb roofed space sized for the 10m2 rule and standard roofing sheets would be fairly cheap too. You could always build it with the option to add a wall or two later if you need it.
Our patio had a pergola with climbers, we've covered half with polycarb and if it wasn't for the southerly winds it'd be great for washing.
