Originally Posted by
LondonAndy
I can't help you with the phone number,
but you are aware that you can normally only upgrade your ticket one class so if you have a World Traveller (economy) ticket you'll generally only be able to upgrade it to World Traveller Plus (premium economy). If you want to use Avios then only certain economy tickets can be upgraded. Clearly cash is more widely accepted
Are there no options in the "Manage My Booking" screen?
This is correct if the OP is flying longhaul ... a not unreasonable assumption giving his/her location.
Of course, shorthaul is two-class and UK domestic single-class. And the point about upgrading only higher Y fares with Avios is true.