Widescreen took a long time to roll out across the BBC (and indeed all channels), and most 1998 shows were 4:3 even after the launch of digital. Demon Headmaster was shown in January so would have been filmed in 1997, when (almost) everything was 4:3.
One of the first series I remember in widescreen was Last of the Summer Wine, in April 1999. BBC News, EastEnders, Top of the Pops etc were all much later.
Most primetime shows went to widescreen in the autumn of 1998 to coincide with the arrival of Sky Digital and ONDigital - loads of shows moved to widescreen when they came back for a new series that autumn, including Watchdog, HIGNFY, Buzzcocks and Noel's House Party (of course, there was that Saturday in March 1998 when the Generation Game, House Party and the lottery all went out in 14:9 on analogue as an experiment) and from then on pretty much all new drama, comedy and entertainment was in widescreen.
Blue Peter went widescreen after its summer break in 1999, as you say the news followed in October 2000 and Pops was very late (thanks to it using ancient facilities in Elstree and it swapping footage with its international versions) in October 2001. And of course Parkinson never went to widescreen before it ended on the Beeb in 2004.
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