Secure Storage for Running Errands
You can get hard shell bicycle storage, but they're usually heavy, expensive and fragile. These panniers on Amazon are typical. Yes, they have a rigid shell and look sort of solid, but in practice the sort of knife that will cut soft-wall panniers will also cut these. Partly because decent panniers are made of quite strong cloth, and partly because really solid panniers end up weighing more than most people are willing to carry. The motorbike "Metal Mule" systems weigh 5 or 6 kg just for the boxes.

For low-value stuff like you're talking about I suggest just using normal panniers and locking those to your bike with a cheap padlock. Make it nice and visible to discourage casual theft - someone can still rummage through them and get stuff out, but they can't just grab the whole pannier. 

The next step would be a metal luggage net that you can put over the panniers and lock to the bike. It's still pretty lightweight and makes it really annoying to get things out of the panniers.

For real security I think you'd need to make something yourself. Buy a box that can be secured and bolt it to your rear rack, probably with a bit of wood between box and rack for reinforcement. Where I live (Australia) there are a lot of those aluminium boxes you see on tradesmen's utes/trucks, and a custom smaller size one for your bike would probably cost about the same as the carbon fibre panniers above. My custom toolbox for home cost me about $200 but it's nearly ten times as big as you'd want to put on a bicycle, a smaller custom one should be under $100.