Gibraltar bins are just like the United Kingdom.
There is 1 large Morrisons in Gibraltar, on Westside road. They leave the dumpsters along the back right hand side of the store next to the road. Those dumpsters are outside around 9pm. A lot of milk products and other stuffs. NO DUMPSTERS ON SATURDAYS.
Everyday there is a fruits and vegetables market on the right of the entrance of the old part of Gibraltar (where there are the bus stops). If you ask sellers they will give you nothing but if you look between 2 and 3 pm in their dumpsters (inside a small construction behind the market and along the street) we will find plenty of delicious fruits and vegetabes. Perfect for raw vegans ! Near the bus stops there is a free WC where you could wash your knife and fill up your bottle.
There is a Eroski supermaket near the border on the Gibraltar side : dumpsters are at the back on the outdoor parking lot, but a lot of employees are around during the day and at night there is a security guy forbidding the access of the parking. Hard to get anything from there. [Edit] I was there for two weeks now in January and it is true this is a hard one but the trick is to go for it very quickly between ca. 22:15, after they are finished throwing stuff away, and ca. 22:40, when the security guard comes out for his shift. You have to be very quickly. Futhermore, right after november they are specially controlling due to the boat hitchhikers camp taking place that month. I think some time afterwards they start relaxing again.