Just additional info hopefully to save you time:
I have called BCC the other day requesting our distance too. Was told that the information is only given in written. My email to enquire on this was answered very promptly!
Our distance (which is quite far) turned to be 0.78 miles less than the returned one on Transport direct link as shortest route. It was definitely easy and worth checking.
Our "official" distance also turned out to be slightly closer. Still not close enough, though!
Well, may be not as good for us to know that we are 0.2 miles on the wrong side of the cut off ;(
Good news actually, especially over such a large distance as it means you're probably very close to the top of the waiting list.