One more way, which you cannot request and can only hope for... sometimes EK does email offers for upgrades a couple of days before departure. That is, they send emails to selected passengers, providing a specific code where the passengers can key in on the EK's website for upgrading to next cabin, at a discounted rate.

How often they do this on LHR-DXB/DXB-HKG routes, I am not sure (but not too optimistic as these routes seem premium demand-heavy). On the route I usually travel on EK (Trans-Tasman), email offers are common (receive them more than half of all times I fly them).

I heard that email upgrades offers are provided to passengers who book on EK's website and are Skyward members. Perhaps someone can verify this.