It is possible that councils do keep a list of people who want an exchange - when my parents were still in a council house (in a different town - different country even, they had a nice one, new built on the edge of Dunfermline, with good immediate neighbours and many friends in various typed of housing. They would not have wanted to move. After I had married and moved out they bought a little bungalow - and then my father was made redundant and had to go down near London to find work , so the bungalow was sold and they were off the property ladder again.
Moving from Portsmouth up to Kirkcaldy was a different story. Someone with a Kirkcaldy council house but working in Portsmouth got in touch with them, having found out they would be moving up there, and an exchange was arranged to his house which he said was "just like this one you are in" - fairly new semi, 3 bedrooms, separate dining area with sliding doors, downstairs loo as well as the upstairs bathroom, garage (though they'd no car) and a very nice garden.
They took his word for it and did not travel up to see it. Arrived by train on 2nd January to a decrepit upper flat in a block of four. One proper bedroom and one small bedroom/dining room off the living room (for a mixed family) ancient bathroom, similar kitchen, half a tiny garden. all in filthy condition, despite him seeing my mother on her knees scrubbing a floor and saying "I left my wife doing that" Overhead clothes pulley in the kitchen with a quarter-inch of grease and dirt on the bars, so many cobwebs on the kitchen window we thought that it was obscured glass.
The moral of this long and boring story is that exchanges need to be carefully monitored so that both parties gain from them. If one party gets a raw deal, they will tell all their friends about it - bad news travels fast.