this is definitely not drying weather.

no, it is not. and we seem destined to have clouds camped over us for the near future.

does it need to be actually sunny to line dry? We've been contemplating putting up a laundry line

depends on the temp, the wind, and the relative humidity...

if you have lots of clouds briskly scudding through but still dryish air, and it's at least 60 degrees, you can dry clothes pretty well.