ITA Matrix only has one stops on the 19th; via Zagreb would be OK since domestic to international is pretty easy there, albeit with a lot of escalators.
If you need a non-stop, Split (SPU) might be your best bet. Four nonstops to London on the 19th; one on Croatia Airlines to LGW, two on BA to LHR and one on BA to LCY. Not sure why BA has ramped up Split and ignored Dubrovnik but that seems to be the way it's currently sceduled.
Split is a five hour bus or ferry ride from Dubrovnik or a four hour drive.