All customer service agents say no - new customers only.
The actual reason is because it requires both migrating to a new account, and a 2.5 Gbit ONT box upgrade.
The 1600 is available if I look it up as a new customer, and verified on Openreach's postcode checker.
Technically, I am eligible to cancel my current 900mbit contract anytime I want as I remain eligible for BT social tariffs, but from what I read, there might be a 1-2 week period of no connection if moving onto 1600 this way.
It would seem prudent for EE to add an upgrade option to 1600 for existing customers on current plans up to 900 if their lines are 1600 capable would it not?
