This site may help - it uses Ordnance Survey software and is essentially identical to the one used by Bucks CC for their distance calucations.
Make sure that you enter the actual addresses, not just the postcode, and then go to Advanced options and select "shortest journey" rather than quickest.
If that establishes that the distance is incorrect you should then make sure that there are no other relevant facts, such as sibling priority, special needs, etc.
If you are still convinced that the allocation is wrong you should contact the Admissions authority for the school (email would be best so that you have a record) and ask them to justify the decision.
They would not be able to get away with withdrawing the offer to the other child, so you should go ahead and query it.