According to the Online Dating Association, a quarter of what it calls “new relationships” in the UK are formed by the use of dating sites. The exact nature of these relationships, how long they last, the methodology used to arrive at the figure of one in four: these things are unknown. The world of dating sites and apps is an apple-and-pears orchard of contestable statistics. In 2013, a study by the Pew Research Centre found that one in five Americans between the ages of 25 and 45 had tried online dating at least once, but at the same time acknowledged that only 5% of Americans who were married or in a long-term relationship had found their partners online. The Guardian’s own Soulmates site says it has 230,000 active users, which was a figure that impressed me until I read that the Tinder app, launched in 2012, was by 2014 registering around a billion “swipes” worldwide a day.

Tinder owes a lot of its remarkable success to a simple movement of the hand. The app’s algorithm provides the user with a stream of likely matches, which he or she then rejects by swiping the screen to the left, or accepts by swiping right. The leftwards movement takes only a second and is literally dismissive; the face vanishes and another takes its place – the user has in his hand the power of emperors, slave-masters and triage surgeons deciding who can and can’t be saved. But at least the rejected never know of their rejection. When dance halls rather than laptop screens or smartphones were the places you went to meet the unknown and desirable, you knew it too well. You walked across the floor of the hall to the side where the girls stood and said to one of them something like, “Would you like to dance?” She might say no. In the years to come you would encounter worse things in your life, but that small humiliation always stood out in the memory: your blush, your retreat back to the male side by an indirect route so your friends wouldn’t notice, the band starting out on Moon River. Whenever you heard or read the word “snub”, this was what you remembered.

Dance halls were the Tinder of their day. In 1953, the Economist described them as Britain’s second-biggest entertainment industry after cinema, with an estimated attendance of about four million a week and 200 million over the year. Football’s 80 or 90 million spectators didn’t come close. The figures for the consequence of all this dancing are, like those for online dating, less reliable: the Daily Mail suggested in 1950 that 70% of couples in Britain had first met on a dance floor, and in Glasgow as high a proportion of marriages were often said to have originated in the same way. But Glasgow was dance-mad. In James Nott’s recently published history of dance halls, Going to the Palais, several authorities speak of the skill of the Glasgow dancer, though somehow nobody has remembered the famous line from a 1949 pantomime sketch, Polly at the Palais: “He says I’m a champ dancer, but I think he’s a damp chancer.” (Spoken by Duncan Macrae in drag, it was still being quoted 20 years later.)

Nott quotes a Glasgow tally for 1952 of 14 permanent dance halls, some of them among Britain’s largest, as well as dozens of other venues licensed for dancing: halls owned by churches, the city corporation, the Co-op and Orange lodges. By the time I got inside a Glasgow dance hall, that figure hadn’t shrunk much – the bigger shrinkage is in the accomplished dancing that now survives, in an overbred, Crufts Show way, in television shows such as Strictly as the last relic of this great social phenomenon. Occasionally a couple might carve a passage through the crowd on the floor like a well-driven dodgem – he in patent leather shoes, steering – but, to quote one of Nott’s witnesses from that time, “The masses are content to shuffle. All they want is to get round [the floor] tolerably comfortably.” What mattered about dancing to the young was that in a more segregated age – inside and outside the workplace – it allowed us to meet and touch members of the opposite sex.

My shuffling days began in Fife. The Kinema Ballroom in Dunfermline, the Raith in Kirkcaldy, the Aberdour Palais. The Palais wasn’t much more than a big shed with a lemonade stall inside, but unlike the Snake Pit (nobody knew it by any other name) near the dockyard in Rosyth, it was felt to be respectable and free of sailors.

Only after I moved to Glasgow was the full splendour of the ballroom revealed. The Locarno, and possibly the Majestic too, had a revolving stage that allowed (say) a band mainly of saxophones to be replaced by a band mainly of guitars, each making music as they swung in or out of view. The Plaza – “the Plaza’s the place” said the adverts – had a fountain in the middle of the floor. No-alcohol polices were strictly enforced. Doormen at the Majestic would come down the queue and turn away anyone they thought might upset the interior decorum, including a friend I was with one night who at most had had two pints of beer. He was a kind and considerate man who introduced me to the music of Brahms, and to my continuing shame, I went inside without him.

This has been history for a very long time. Few dance halls survived by the end of the 1960s. Some lived on a little longer by restyling themselves as discotheques or nightclubs (Tiffany’s, Joanna’s); others became bingo venues; many were demolished. What I hadn’t realised until I read Nott’s account was how swift the transition had been from boom to bust. Throughout the 1950s an entertainment that had sprung to life between the wars went on expanding. It employed 50,000 dance musicians and made good profits for dance-hall chains such as Mecca (a carefree name, in hindsight, for a company devoted to dancing, gambling and beauty contests). “The boom at the Palais is fantastic,” Mecca reported in 1960. “Our business increases by 10%.” Its shares trebled in value between 1958 and 1962 as it opened new halls throughout Britain. Unlike the cinema, which thanks to television had seen a steep fall in numbers, dancing had no obvious rival.

Nott’s explanation for its downfall is that a new era of prosperity and job security had turned the working class “away from such communal pleasures and towards homebuying, homemaking, family life and ‘individualism’”. That may well be part of it, but I think a bigger reason was the slow but steady erosion of male/female separation. Tom Harrisson, one the founders of the Mass Observation, is quoted memorably in the book when he writes of young men coming to prewar dance halls “perhaps wanting love, but very vaguely”. A different male generation began to realise that you met women as you met men – randomly, by odd routes, at work, in pubs (where they were much more present), as the friends of friends, in circumstances where you were relieved of the ulterior motive and the silly hope that something might come of it when the last number ended and you asked the second most important question of the night: can I see you home?

Going to the Palais: A Social and Cultural History of Dancing and Dance Halls in Britain, 1918-1960, by James Nott is published by Oxford University Press.