There are more of these than I thought (including codeshares, which count for the purpose of this guessing game). From the BA website (the number is the LHR terminal):-
Aberdeen - 1
Amsterdam - 4
Athens - 1
Barcelona - 1 or 2
Brussels - 4
Budapest - 1
Dublin - 1
Edinburgh - 1
Geneva - 4
Gibraltar - 1
Glasgow - 1
Houston - 4
Kiev - 1
Madrid - 1 or 2
Malaga - 1
Manchester - 1
Marrakech - 1
Newcastle - 1
Nice - 1
Prague - 1
Rome - Fiumicino - 1
Seville - 2
Zurich - 4
On this hypothesis, one could discount DUB because you can't buy a LON-originating ticket on the EI flights concerned.
And that's just BA. However, to do the exercise properly, I suppose that you'd also have to list all the destinations to which you can fly from both LHR and LGW on carriers that will sell cheap one-ways, to allow for the possibility that the trip has been built on two one-way tickets on different airlines.
Given that many of these places are pretty standard fare for stag weekends, I suppose the short answer for the OP is "I haven't got a clue!"
