BHX is about the same with 80% or thereabouts loads on their EK flights, especially since the increase in Mid East capacity at MAN - I agree with Ringwayman, I think EK put the 777 on to cope with cargo loads. Just like BHX, I bet NCL will see also its fair share of 777-200 as well as low density 300's, BHX gets a lot of the latter.
As for EDI, agree with Skipness, am sure it's on EK's radar but certainly not in the next 12 months or so based on capacity increases at GLA and NCL. Look at how well LGW has done in attracting new airlines since being sold (altho they have lost Air Asia X), am sure it will be the same at EDI
Don't hold your breath on TK, as I have said before they went on about going into BHX for 2 years or so before they actually did and put into print in the public domain that were would start GLA flights but these never materialised. Again, EDI is def on the radar but when it actually happens that could be a while too!