But most line managers and a lot of executive level managers have literally never had any training in management, so sometimes they're just copying bad behaviours from people above/around them, even when they were things they themselves hated before getting promoted.
A "I'm working as fast as I can. These interruptions are not helping. You can help get it sorted faster by keeping people off my back - I promise to update you as soon as I know anything" can be enough. Carry through, and give them enough to go back to their boss with to keep them away, and show them it actually lets you fix the problem, and thank them for helping afterwards, and they'll soon learn to prefer shielding you.