Or even see if Dave Reid will let you use his route lookup service at http://www.flightroutelookup.com/FlightRoute/
FlightRouteLookup.com is open to all.
<?xml version="1.0" encoding="utf-8" ?>
<Flight>
<FlightNumber>SHT9P</FlightNumber>
<Callsign>Shuttle 9P</Callsign>
<Leg>
<Origin>
<ICAOCode>EGPH</ICAOCode>
<IATACode>EDI</IATACode>
<AirportName>EDINBURGH/TURNHOUSE</AirportName>
<Country>UNITED KINGDOM</Country>
</Origin>
<Destination>
<ICAOCode>EGLL</ICAOCode>
<IATACode>LHR</IATACode>
<AirportName>LONDON/HEATHROW</AirportName>
<Country>UNITED KINGDOM</Country>
</Destination>
<GCDistanceNM>288</GCDistanceNM>
<DistanceFromOriginNM>251</DistanceFromOriginNM>
<DistanceFromDestinationNM>38</DistanceFromDestinationNM>
</Leg>
</Flight>