On Sunday 4 January, after a mere 40 years, BBC Parliament is repeating the BBC's live coverage of the 1964 general election results. It marks the coming of a new prime minister and the adieu of an old anchorman. The PM, of course, is Harold Wilson. The anchor is Richard Dimbleby, father of both Dimblebys, big, balding, fiftysomething, dressed in glasses, a dark suit and with a white poc-ket handkerchief. You could weigh this man's authority. His speciality is jokiness (demonstrating to viewers at 4am that he is not wearing pyjamas below the waist), but it is the humour of the top man, the popular headmaster whom the boys know is not afraid to use the cane.

"It is 9.25 on election day. The nation has voted. The count is on," he begins promisingly. We are immediately in another era, one in which the ballots close at nine, when there are no exit polls and where Steptoe and Son has just finished (postponed by a half-hour to give Labour supporters time to vote). The studio is dark and undecorated except for a large scoreboard up beyond Dimbleby's head. When by the next day it is clear Labour's majority is going to be tiny, but not how tiny, we cross to it nervously every few minutes. The technology is not up to delivering on-screen graphics; even the results cards are filled out by hand. And there are pitifully few outside broadcasts at the counts. When we do get out of the studio, it is usually to sepulchral party headquarters or to Alan Whicker at Trafalgar Square, where revellers are splashing about in the fountains. "Not unlike one of those Brock benefit fireworks events," as Dimbleby says.

Back at TV Centre, the performers are clustered on two levels. Downstairs sits Dimbleby with, on his right, Ian Treth-owan, the BBC's serious, waistcoated political commentator, and on his left the tense, abrupt academic David Butler. With the swing fluctuating violently, Butler is not having a good night. He says things like "I'd rather have a few more minutes with the figures, if you don't mind". Upstairs is his rival Bob McKenzie, the talkative, deep-voiced Canadian political scientist who lists "broadcasting" as his hobby in Who's Who. There is not one woman on the set, except among the scores of clerks in the background dressed, as Dimbleby tells us, in terracotta overalls to make the "poor little things", less "conspicuous". He pauses in the early hours to let the cameras ogle them.

This is Britain and the BBC on the cusp between postwar deference and the country as permanently re-ordered by the 1960s. Clement Attlee, frail but candid, gamely comes to the studio to praise Wilson. The Liberals, despite Eric Lubbock's triumph at the Orpington by-election in 1962, are far from being represented in every constituency. The Tory politicians have old-time names: Brigadier Todd Hunter, Captain Litchfield, Wing Commander Bullus, Dames Edith Pitt and Patricia Hornsby-Smith. Labour's MPs are called Ray, Bessie, George and Fenner.

But as they go on air on Thursday news breaks that Nikita Khrushchev has been deposed in Russia. Before the presenters sign off on Friday China has exploded its first atomic bomb. Listen hard and you hear the drumbeat of the social revolution to come. Scolding Liverpool for a low turnout, Dimbleby says: "Thinking about the Beatles, I should think," and the night's coverage ends with "A Hard Day's Night" playing against atmospheric, Saturday Night and Sunday Morning-style shots of a studio by now covered in discarded paper and ash. The new PM who like the Beatles combines grit and glamour, does not speak with the customary stuffiness of high office. Asked at midnight how he feels he says, "Quite frankly, I feel like a drink."

More even than David Frost, who delivers a lame monologue about the parties he has been to, the truly coming man, Robin Day, is up in another eyrie. His wordy courtesies barely conceal the insolence towards authority that will become the standard for interviewers. On Friday he questions a hungover George Brown. The interview ends with Brown warning him not to interrupt so much next time: "I like you immensely but you must understand how we do these things." "May I call you 'brother'?" Day cheeks back. "Goodbye - Brother Day," he signs off.

Dimbleby can't quite believe what he's heard. "Three rousing good cheers and a happy Christmas to all our readers," is all he can say. I fear this is as lively as he gets. For most of the first night he reads the results like a glorified returning officer. When he is warned that it may take until the following afternoon for the result to be clear he mutters wearily, "If we live."

The words have a macabre echo, as before there can be another election to secure Labour's majority, Dimbleby will indeed be dead, and he knows it. His cancer may explain the curiously funereal air of the night-time broadcast. Fortunately, the mood lifts the next day. Fortunately, too, there is a brilliant young reporter reporting from Euston Station where the new PM's train is pulling in. His name is David. In 15 years' time he will anchor election night. BBC Parliament plans to show us in May, on the 25th anniversary of another political sea change, how he did in comparison with his dad. I can't wait.

Andrew Billen is a staff writer on the Times