It shouldn't matter which airport they send it to as they will deliver it to your door. My experience with IB lost luggage is that it's generally there within a couple days but given how things are in London right now, maybe a bit more. Granted I live in Madrid, but between the BA/IB tie-up and the fact that IB has a pretty big operation itself in London, I'd imagine they should get it too you probably by the end of the week.

The more annoying thing with them will be getting the EU261 comp