I’d be inclined to say that Air India's return won’t have that much of a detrimental effect on EK’s loads as primarily they are targeting the BHX-ATQ traffic
I think the one to feel the most immediate effect will be T5 - their route from BHX survives on ATQ transit pax, there is very little demand to go to Ashgabat itself (have you tried getting a visa, it's quite complicated!) and they don't have many other onward connections either. I hope they stick around, they have been very loyal to BHX through tough times in the past. The presence of AI will be tough for them, given that this time round AI have to fill their planes entirely on BHX O&D traffic with no transit pax to rely on to/from YYZ.
The presence of TK will also affect this third generation AI operation, they offer good connections and competitive fares to India from BHX - and I should imagine a double daily BHX-IST can't be too far away. I guess a lot will come down to price, AI lead in fares on their website are attractive and although I find TK a very good airline I would personally rather fly non stop to DEL given the option than change aircrafts.
EK - I think they have sufficient other onward connections to survive but as pointed out pax that may have used them for DEL might now be tempted to AI. I know that there are often a lot of Indian connections on these flights, it will be interesting to see who they choose from 1st Aug.
QR - I think with AI starting BHX will be pushed even further down their list of priorities now.
AI need to run a reliable and punctual operation at BHX - I like others am thrilled they are back and I hope this time it's for the duration and that it's not just a proving route for their 787 before they on a whim find somewhere else for it to fly....I look forward to seeing pictures from this Thursdays launch day (assuming no more Dreamliner oven fires.....)