According to her school, my dd is several years ahead of her classmates, but I have always been very happy with the school's approach to dealing with this. They did suggest putting her up a year at the end of reception, but we declined - she is young in her year anyway, and acceleration by a year would still have left a gap between dd and the other kids. So she has stayed with her peer group and is blissfully happy with lots of friends.
So far, the teachers have all been good at differentiating work for her. Could she achieve more if pushed a little harder? Absolutely she could, and if we wanted to hothouse her, who knows what heights she could reach?! But she is six! At the moment, she likes school, she likes learning and she likes playing with her friends. She is making progress all the time, but I don't want her to be racing too far ahead of her friends - yes, she could probably rush ahead and get lots of qualifications at an early age, but to what avail? What would be the point.
As far as I'm concerned, bright kids need enrichment rather than acceleration, and in my own experience, most teachers seem to be quite good at providing this. I think most are also keen to ensure that kids make the expected level of progress as defined by the government, but as a parent, I wouldn't necessarily measured by NC levels!
If your child is bored in school, I would talk to the teacher about what might interest/motivate him, but I wouldn't get too hung up on the issue of "giftedness" and would also look at what you can do to enrich his life in other ways.