They'll continue as long as people don't have card machines or access to internet banking. The Dandie Dinmont Club, The Irish Wolfhound Club ,my gardener, my decorators, and other minor contractors, only accept cheques. All right, the gardener would take cash, but that's because he's here on site at the time and I'm usually here too, not miles away.
It`ll be quite a while yet before cheques disappear. There are plenty of postal savings accounts about. I have a postal ISA and I found that I could also make deposits via my online banking and the ISA company actively tried to discourage me, saying that they preferred cheques.