Have you priced up starting your trip in VIE and ending in LHR as sometimes it can be cheaper or not much more to end in LHR for example just done a trip to New York and it was £20 cheaper to end at LHR,also have a MAD BOM LHR that was £25 more to end in LHR but saves all the hassle of going back to MAD.
I have done quite a few BA holiday bookings with a car and not once have i collected it never had any problems.