Been there, got several t-shirts. DD was very ahead and we had all sorts of promises from the school but they didn't have the time or resources to deliver them.
It all hit the fan for us in year 2 as well with a teacher who just wasn't prepared to do anything - funnily enough at almost exactly this point in the year. We ended up moving her to a smaller school that had a good reputation, funnily enough, for SEN and so were prepared to be more flexible. This worked for a few years (she did comprehension while other kids were reading to the teacher for example). With hindsight, she was struggling again from Year 5 and I wished we had done more.
She's now 17, and very happy in a selective secondary school. She didn't level out - was top in the entrance exam and has done very well since. So for all the people thinking about this, it's worked brilliantly for us - not just academically but also giving her a social group of kids more like her.
Other things I would suggest.
Firstly, if you can get her maths and reading age tested by the school (or someone else) it really helps persuade them. DD was tested by the ed psych (first school were convinced that she had a problem, rather than that she was bored). Knowing that she had a reading age of 11 in year 1, meant they couldn't not see the issue.
Secondly, if you can send resources in, it really helps. We used Life of Fred books for both English and maths - they are designed to be used by homeschooled kids on their own so she could work through it and then talk to the teachers about what she was doing. But there are loads of other options.
We did focus on other things - everything from Brownies to art clubs to ballet - but those didn't solve the boredom in school time. Then - would be much harder now - we could take her out of school one day a week to do forest school which was brilliant for her.