We received a letter from our first choice school outlining why my son's application had been rejected. The letter stated that he did not attend a feeder school and that only children attending one of the feeder schools had been admitted - the furthest away child being 5 miles from the school.
My child does attend a feeder school (it is listed with its address and postcode in the Admissions Policy document attached to the rejection letter). We live 4.13 miles from the school. There is no indication in the Admissions Policy that there is any preference between feeder schools but ours appears at number 16 in a non-alphabetical list of 27 schools.
We would still very much like our son to attend this school; notwithstanding their administrative incompetence! 
What should my next step be? Currently I have accepted an offer from our second choice school. I don't know if it makes any difference but the school is in a different LA to the one we live in.