Even if you discovered there was a by-law about laundry, your neighboring EC is not compelled to enforce it. And since a duplex has only two owners, your chances of getting anyone to change their habits are slightly less than zero. I doubt your local council will take a position on this so there’s not really very much you can do.
There may be a remote chance of taking legal action on the grounds that the ‘visual pollution’ of their washing is lowering the value of your property but I wouldn’t recommend it. In fact I suspect this is one of those cases where the misery associated with getting a result outweighs the slight benefit of whatever result you might get.
In other words, if you can, learn to live with it