This is bullying. Yes, of course talk to the teacher. Poor lad. 
And to prevent your son turning into a snob like his peers, I definitely wouldn't swap over to a more expensive brand. I'd encourage him to rise above it and to be thankful his parents have the sense not to spend £s extra for a brand name. He shouldn't have to change who he is to fit in. If the children are horrible to him about a food label, then they aren't worthy enough to be his friends. Who on earth would want friends like that? I certainly wouldn't.
I got this with 5yodd (normal non-private school). I sent her in with pineapple chunks for snack time. One boy told her he was 'allergic' to them and started saying things like 'yuck! Stay away from me.' This then triggered the other children to do the same. No one wanted to play with her when she was eating pineapple chunks. So i then decided to send dd in with strawberries instead. Surprise, surprise, the children were 'allergic' to these too. Same with bananas. Same with tangerines. Etc etc.
In the end I spoke to the teacher. In turn, she spoke to the class. So far, so good.
If children want to bully someone, they will. Go ahead and upgrade your son's lunchbox. But next week he'll be getting picked on for something else. Then something else. It's not him that has to change. It's the attitudes of the other children. And the first step in doing this is talking to the teacher.
I also don't get why so many posters are telling you to accept this as it 'comes' with private schools.
Regardless of which type of school a child attends, no one should have to put up with daily bullying.