It is totally possible to get a $4 lunch in the UK.
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.
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.