You could also ask the SK agent at UME to call BA so that they have your BP ready for you at the gate (in case UME is unable to print the BP even to LHR, which I doubt). And as jacob_m said, your baggage will be checked through, although if it will make it is perhaps another story.

If this fails, then you should go to the transfer desk at ARN. But if your flight to ARN is late, then do as jacob_m suggested and try to do the BA check-in on-line after having checked in at UME.