Part of IAG's strategy is joint procurement and interoperability. I am led to understand that this will see the same J seats being fitted across all the companies and a/c types. Given that IB just fitted new J seats, it's not beyond the realm of possibility that BA will end up using theirs.
I for one would be glad - I love the IB hard and soft product (though not mad about the lounge) and have switched most of my TLV-NYC to go via MAD instead of London now, which also saves me nearly $1,000 on a typical I-class. Just shows that price doesn't correlate directly with either route or cabin capacity. I suspect much of this cost difference is the LHR/YQ/APD premium.