Wiki and Transdiffusion say 1968.
Radiosoundsfamiliar.com says 1969.
It was 1968, when the new franchises came in. TV Times started with ITV in 1955 but the individual regions could contract them out to other companies if they wanted, hence Rediffusion and Granada always had TV Times but other companies like Scottish and Westward had their own (although actually The Viewer for STV and Look Westward were published by the same company and were basically the same magazine).
In the Midlands, ATV initially had TV Times but in 1964 they actually lost the rights and ATV gave them to another magazine called TV World (in one of the sixties MOTD repeats they showed on BT last week, there was a TV World hoarding at one of the grounds). Although as I remember looking at in Birmingham Library when I used to live in Birmingham, TV Times did carry on publishing in the Midlands for a few weeks, but minus any listings, in the hope the articles themselves might be enough of a draw. But they weren't and it closed down after a few weeks.
Anyway, as part of the new franchises in 1968 it was a condition that all regions had to use the TV Times, except for Channel of course who were allowed to do their own to give them a bit more cash.
It's not correct that they used to be more precise in the listings, though, TSW famously used to bill things starting at 3.27 and 10.34 but they were the only region who did so. There would be just as much rounding up and down as there is now. Indeed, I've got a Radio Times from 1983 where there's a letter complaining about Invasion of the Body Snatchers starting on BBC2 before Doctor Who had finished on BBC1, and the reply says they try to avoid that wherever possible, to the extent of asking live programmes to carry on for a few more minutes to hit a common junction. So they would have been inaccurate quite frequently.
And I don't see the need to give exact times anyway, you're not catching a train. And who's recording The One Show?