[James2001]

And, as Michael says, the Television Centre logo was changed pretty much as soon as possible - you can see the new logo (Television Centre wording and all) in episode six of I'm Alan Partridge, which was transmitted 08/12/1997. I think it's safe to assume there was a turnaround of a week or two - so the logo must have been installed by at least late-November, if not earlier.

Unless it's a dodgy memory, I think I remember that the scaffolding could be seen at the front of Television Centre at the start of that year's Children in Need show.

The new sign was up for Children In Need, there was a programme where you could see the scaffolding though... I think it was something with Hale & Pace and Eurovision. Was trailed quite a lot, and you could see the scaffolding on one of the clips in the trailer, so I remember seeing a lot of it.

Looking at Genome, this seems to fit. Aired in May 1998, but likely filmed months earlier:
genome.ch.bbc.co.uk