Welcome to FT MattUK81!
So if you want upgrade your second flight I think the most likely way you can do this is using avios. In order to check whether an avios upgrade is available there are two things you ought to do.
1. Have a check what selling class you are in, they should all be upgradable unless you are in O, Q, or G. You can find this by going in to manage my booking, click on the flight, and click on "More flight information" which should show selling class.
2. Check whether there are any club reward seats available on your flight. Just do a reward search via your BAEC homepage for the second flight only and see if club seats are shown.
If you manage to get past 1 and 2 then you will have to call to do the upgrade with avios,