What's the Name of That Book??? discussion

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Daz 4 Zoe
SOLVED: Children's/YA
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SOLVED. 80s British futuristic YA - cities surrounded by walls to keep out the "undesirables" [s]
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It's set in Britain in the future. For some reason, all the cities now have walls or security fences around them to keep out the "lower classes" or undesirable people. Inside the cities the people have lots of food, good schools, nice houses, etc. But outside there is a lot of crime and not enough food.
The story is about a girl from a city who somehow meets a boy from outside (possibly he and friends snuck into the city somehow?). She thinks he's a thug, but then she realises that he's not actually a bad person and they develop a relationship (don't ask me how).
The guy's name was Baz or Gaz (which is my only clue that it's British). I can't remember the girl's name.
Any ideas?