If you buy a flat with these rules and do put your washing out, out of interest, what powers do they have to stop you? (Appreciate tenants are different).
The Management company can warn you but ultimately there is nothing they can do.
If, as the owner of a leasehold property, you do not abide by the terms of your lease, the freeholder can confiscate your property from you. You have broken the terms of the contract, therefore it is null and void, you don't get a refund of the money you paid for your flat.
I first heard of this in the case of a woman on the South Coast who did not pay her flat management charge, despite being given every opportunity to. The outcome of legal proceedings what that the freeholder (who was the original developer) repossessed her property and she lost all of her purchase price, as far as I understand it.
In the development were I live, management committee are currently taking a flat-owner to court in an attempt to take her flat off her. (Her breach is much more severe than aforementioned case, don't want to give details as not sure of implications.) Obviously the court case will costs thousands/tens of thousands, but as the flat is worth several hundred thousand, they will more than get their money back if they win.
I'm not saying that anyone has ever had a flat worth several hundred thousand pounds confiscated as a result of displaying laundry, but it appears that it is a legal possibility, so it is a valid answer to the question "what can they do to you, if you are the owner."