It's a bit of madness. But we have seen other signs of madness herhere, like a company following you to the loo to make sure you don't take any phone interviews. That kind of madness is against you. Your company's madness is actually good for you.
You may not like it, mostly because you are not used to it, but what they do is in the end good for your health. So don't fight it, but embrace it. Yes, you will get less work done in an eight hour day. They must realise that (if they complain, then you can point out how your work is interrupted).
A very good technique how to do your demanding job without stressing out: You arrive at your desk in the morning. You pick the most important item that you should do today, and you do it. You completely ignore the second, third, and so on important items. And in the evening, you go home. You don't stay longer, you don't worry if you are interrupted by health and safety. The next morning, you arrive, but the state of your task list is a tiny bit better.
BTW. Make sure you have a good desk, a good chair, good lighting, a good keyboard, a good monitor. There are places where getting these can be a major fight. In your place, they should supply all these without many questions asked.