Went through exactly the same thing when I moved with my OH 8 years ago. Although not 6m away, we were more than a mile away from the catchment boundaries and as it's a massive school, I was told that there would no problem as all the kids in our area went to that school. We were turned down and offered a school totally in the opposite direction which has just been inspected by Ofsted and deemed inadequate.
What happened is that the other school had been facing issues for a few years. As a result, parents in the catchment area of that school had worked out that if they put their kids for the infant school of our local area, they would get priority getting a place in the local senior school, which had been rated by ofted as Excellent. As there were three feeder schools, getting a place in the infant school wasn't a problem. As a result, anyone moving into the area, even in front of the senior school found that they couldn't get a place, whilst a larger number of pupils travelled every day from miles away.
I was horrified at the idea of sending my kids to the other school, especially as they came from an excellent school, but we were advised to visit it as the pupils and teachers were lovely and the issue was with management. We did so and loved the school. We were met by the new Head Teacher who seemed excellent.
My kids moved there and they couldn't have received better schooling. The Head turned the school around and my kids achieved very highly. The irony is that the Head of the school left shortly afterwards and the school took a massive tumbling down. 3 years later, why my DS moved to secondary, his school was rated as good whilst the 'Excellent' school was put under remedial measures! It really shows how things can turn around very quickly and in the end, I'm delighted that my kids didn't get a place there even though the logistics to drop them/pick them up was a nightmare.