Last time I did this, for a redundant settee, I sent a request via text to the number given. In due course, I received a reply telling me to put the item out on the street beside the bins on the evening before collection day, which I did. Next morning, it had gone - but whether the council took it or the white van men got there first, I have no idea.
As has been said, for white goods, if you are buying a new dishwasher/washing machine/fridge etc then usually they will deliver the new and take the old away with them. This is certainly true of Euronics, who are hard to beat anyway.