They might be a bit surprised at first. Maybe Tony makes some jokes about British tea and bad teeth, but in a friendly way. Steve would probably be intrigued by Peter's different cultural background and might ask him about British history.
The Avengers' reactions would be quite diverse. Bruce might be interested in any scientific differences in Peter's education due to the British system. Wanda could be curious about British magic or folklore that Peter might have been exposed to growing up. Vision, on the other hand, would analyze the cultural implications of Peter being British in a very matter - of - fact way. And Peter, being Peter, would probably take their reactions in stride and continue to be the friendly neighborhood Spider - Man, just with a British twist.
Well, initially some of the Avengers could be taken aback. Thor, for example, might not fully understand what it means to be British. Natasha, being the perceptive one, would quickly adapt and start using Peter's Britishness to her advantage in some undercover mission planning. Clint might tease Peter about his accent. Overall, they would gradually accept it as just another part of who Peter is.
They could react with surprise. After all, Peter is still young. But then they would likely be happy for him. Maybe they'd offer to take MJ out for a nice dinner to get to know her better.
There could be a plot where Peter's family in Britain is in danger and the Avengers have to help. This would involve them learning more about his British roots and his family life there. Also, perhaps Peter has a British accent that only comes out when he's really excited or angry, and the Avengers are constantly trying to make him show it.
In many fanfictions, the Avengers' reactions vary. Tony Stark might be proud, like he's found a protege. He'd probably start upgrading Peter's suit right away. Captain America, on the other hand, would be more concerned about Peter's moral compass and whether he's ready to be a full - fledged Avenger. Hulk might not care much at first, but once he sees Peter's strength, he could become his ally. Overall, it's a mix of different emotions and actions.
Peter might be really nervous at first. He's used to being just the friendly neighborhood Spider - Man, and now the Avengers know he's Tony's son. He could be worried about living up to their expectations.
Tony Stark might use his quick wit and technology. He could immediately scan Peter to make sure there's no physical danger causing the hyperventilation. Then he'd probably crack a joke to try and calm Peter down, like 'Kid, you breathe any faster and you'll fly away like a human jetpack.'
One way is by getting involved in Peter's school life in a more official capacity. Maybe they could arrange for some anti - bullying seminars at the school. Natasha could also train Peter in stealth and evasion techniques so that he can avoid the bullies more easily. Thor could even offer to be Peter's bodyguard for a while, at least until the bullying situation is resolved.
Natasha Romanoff could show her emotions in a more subtle way. She might look at Peter's old things and a small smile would cross her face as she remembers his innocence and determination. Thor, on the other hand, might become more determined to protect the world in Peter's honor, as he respected Peter's strength despite his young age.
Peter is likely to be in awe. He might be a bit nervous at first, but also extremely excited. He has looked up to the Avengers for a long time, so meeting them would be like a dream come true. He would probably be stuttering a bit as he tries to introduce himself and show his respect.
He might also get angry. Peter has a strong sense of justice. If he feels that the Avengers are being unfair, he could stand up to them. He'll use his quick wit and his powers to show that he's not going to be pushed around easily.
The Avengers would initially be in shock when they find out Peter is sick. Clint Barton would be the one to keep a calm head and start organizing things. Wanda Maximoff would try to use her powers to ease Peter's pain if possible. Vision would use his vast knowledge to try and find a solution. They would all be very concerned and do everything they can to make Peter better, from getting the best medical help to providing a safe and comfortable environment for him to recover.