This implies that they stopped fighting, and after that, you couldn't eat because you were upset. Let me change this to American English. "I couldn't eat my supper because my friends had been having a fight for hours." = They finally stopped fighting, but you were then too upset to eat. "I couldn't eat my supper because my friends were having a fight for hours."= Their fighting kept you from eating because they were fighting at the same time you were trying to eat.

Think about this example sentence: "When supper time came round, my friends had been having a row for hours, and I couldn't start eating in those circumstances." This is a correct usage of the past perfect continuous. In my case, the fight was continuing at the time you wanted to start eating. I agree with Tempus's comments too.