I have had the letter back today telling us that S isn't eligible for free school transport as we live less than 3 miles away from the school.
I have rung to ask how far away we actually are as it didn't say so on the letter and we are 2.97 miles.
The woman I spoke to was very nice and has said that she will run the check again for me tomorrow and email me to let me know. I doubt it will change - the house isn't going to suddenly move during the night.