[Stooky Bill]

I'd suggest it may have been known earlier in the day that he was very unwell / taken to hospital, and that things weren't looking good. This might have prompted a few 'precautionary' measures, such as removing the ID and preparing a playlist for potential near-future use. It's also some people may have heard unofficially and/or directly from Steve's family prior to 5pm, hence how Jeremy Vine may have been aware by 2pm. The BBC would have also needed some time to prepare a statements to release with the news.

It's quite possible that Sara Cox and her colleagues only found that he'd died out once she'd handed over to the 5pm news. Perhaps fortunately the bulletin was about 5 minutes long, compared to the usual short midday bulletin at the start of Vine's show. This would fit in with what Mike Powell has said on twitter about him only knowing as he read it out.

He died on Monday so there was no doubt, it was just a case of when it was being announced and co-ordinating that. BBC News announced it onlime at the same time as Radio 2 with a prepared article (it was an actual article, not just the one liner that sometimes appears).

As I say Sara's show did seem to change tone leading up to the news and she didn't promote ahead except to say the news was coming up. The newsreader first saw it in the bulletin, but there's no way that Sara and team had no idea till then.

They almost certainly started working on getting some songs together as soon as word had reached Radio 2 earlier in the day. But the on air studio would have known before the news, 2 minutes isn't a great amount of time to tell them, let them get used to it, load the next couple of songs and prepare what to say in the next link.

You don't just walk into a studio and say 'your colleague's died, you're back on air in 2 minutes say something nice and play this song'