I'm sorry to read you have just fallen short due to distance for QEHS!!
When I called about distance last yr I spoke with a lovely lady in admissions at Lincolnshire County Council who informed me they use the Map Point System which is very accurate. She took my postcode and number of house and it came in at 13.502 and when I had checked on google maps it was 14.4. This meant we opted to try for Caistor after looking historically at how far they had stretched on previous yrs.
I think if I was you I would be inclined to phone them back and ask them to check again for peace of mind.