The 767, but that might have too much capacity. (And, of course, good luck getting BA to sell you any new ones to supplement your existing fleet). Or, the A321LR.

ORD-EDI is 3226nm. I suspect that's well within the 4000nm range of the A321LR, year-round, although I will admit I could be wrong.

It's the XLR in particular that I don't understand the need for; if they're not looking to run significantly longer routes than the A321LR would reach, I don't know why you'd pay extra for the supplemental fuel capacity.