What Riven said. Fossie, there is no reason on earth to think that if your kids are "bright" (I assume you mean of above average academic ability) that they will fail to achieve their full potential at a school where the majority of pupils are not. You might have cause for concern if your children were average-ability "plodders" who would require a great deal of support to achieve level 5 at KS2, for example.
We won an appeal for my 13 year old DS to join a very popular and over-subscribed comprehensive school when we moved a few months ago. We had to write a detailed 3 page letter in support of our appeal and we had to attend an appeals panel and give a half-hour presentation to 6 people stating our case.
DS is very shy and had been badly bullied for being a "posh geek" at his previous state school. We argued that he needed a school which had high academic standards and excellent pastoral care, and provided letters in support of his application from his GP and from the anti-bullying charity Kidscape (where he'd attended an anti-bullying workshop) stating that his mental health had been adversely affected by his experiences.
We argued that he needed a very local school because he a) was phobic about using public tranport on his own after being attacked on the bus while travelling to his previous school, b) we are a non-driving/car-owning family) c) he finds it hard to make friends, we had just moved to the city and it was important he went to a school where he would hook up with kids who live locally.
We said we would home-ed if he wasn't offered a place at this particular school.
We stressed that DS's interests and abilities were in line with the academic specialisms and after-school activities offered by the school.
We discovered the exact number of pupil figures for each year group over the previous 5 years, and pointed out that they had in fact been able to admit more than the stated limit of pupils per year without adverse affects on Health and Safety, or on the school's academic results.
We visited the school with DS and had an interview with the headmaster prior to our application. We followed up the visit with an email AND a letter to the headmaster thanking him for his time, expressing our admiration of the school, our intention to apply for a place and offering to assist with extra-curricular activities.
We phoned the school admissions officer on a daily basis to check progress of our application and basically made bloody nuisances of ourselves.
We won. But please be aware of how very very difficult it is to win admission appeals. It is an exhausting procedure and is designed to make sure that only the most deserving cases (and even then, sadly, often only those with the most tenacious and well-informed parents) get through.