It's my understanding that it's 12:01am in the city you are flying from. I know I have to argue this point with phone agents upgrading from YYZ and they were in Winnipeg. Since to them it was only 11:00pm they tried to tell me to call back in a hour. I had to correct them on the rule.

Or for instance if you were doing a quick turn around and only wanted to upgrade your return portion you would use LHR time to calculate the 4 day window.

You very well may be able to try and use eastern time.. but it's not the rules as I understand them.