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Would that be on one PNR or two separate ones?
While it should be ok if all goes to plan, there are potential problems in those cases if on separate PNRs.
The first is that you need to make sure that you have all of your documentation about your onwards journey at hand at LHR or BA may not let you fly because for them you would be going to DME and would need a visa.
The second potential problem is what happens if you can't OLCI for your CX flight. I don't know if they have a transfer desk at DME and if not, it could spell trouble as you would not be able to go landside to the check in counters.
The third and last possible problem is a variation on no2 which is what happens if BA refuses to through check your luggage? They are sometimes a bit funny on through checking luggage on separate itineraries (although normally they are of course nicer when the two itineraries are both OW) and again, you would not be able to go landside without a visa.