Welcome to FlyerTalk grand_canyon!

No premium economy on AA, so fortunately upgrades are from economy to business. For a brief summary see the AA wiki. Upgrading on the return from LHR also requires an extra £60 APD tax.

Upgrade availability is in C class. You can find this on Expert Flyer (go to Flight Availability then Award & Upgrade search tool). They have a free trial that might be enough if you can find availability now before you book. If there is no current availability you can be waitlisted, but elites will be ahead of you in priority.

BA (like AA international flights) only op up when oversold, and usually in order of status. So you were very lucky to get an up up without status, and doing this both ways is almost unheard of! So next time, probably no upgrades.