You can get pre-packaged sandwiches in the US (and a bunch of other stuff too, including hot food). I don't buy them and don't know the exact price, but they aren't expensive, definitely under $5. Eating from corner stores and gas stations is just usually looked down on.
Pre-packaged sandwiches in the US are typically more in the $8-10 range, and that's just for the (sad) sandwich. It also tends to be much more depressing than what you'd get in the UK. Barely edible.
Basic pre-packaged sandwiches can be had for under $2.
For about $4.75 you can get a sandwich, pastry, and a latte from just about any of the chain corner shops (Tesco Express etc)
It's not gourmet, but it's a solid affordable option that millions of people eat every day. There's no real equivalent of this in the US sadly.