Government expectations
I love the comment from the government reported by the BBC - "The government has said it took BT nearly three hours to alert ministers to the problems it was experiencing."
which seems like a typical non-technical failure to grasp the idea of priorities. If the issue started at 08:30 on Sunday I'd take a wild guess that the only relevant BT staff working (either actively or on call) would be the engineers, and they'd be busy trying to fix the problem. They're engineers, so they're sure as hell not gonna be calling Whitehall who likely can't contribute anything practical to fixing the issue, they'll just be updating their immediately line managers. I imagine you'll have to go up a few levels of management (none of whom would be actively working on a Sunday morning, so possibly not immediately contactable) before you reach someone with the authority to speak direct to the government on behalf of BT. They don't indicate whether any status pages or similar were updated with information, but that's presumably more likely to happen in the short term, than finding someone willing and senior enough to place the call, especially when initially they'd likely have zero information to pass on anyway.
Standard "I can speak to you about the issue, or I can fix the issue... I can't do both".