If you are travelling with a partner though there is no way of seeing the available seat plan before you complete the upgrade, it could be available seats are across decks let alone cabins and there is no return from the booking after you have paid
There is one way of seeing the available seats before committing to the upgrade.
Go to the BA website and make a dummy booking for the flights you are on, opting for the class you wish to upgrade to.
Once you've chosen the flights and before you have to enter any personal or payment details, you can choose your seats and you get to see the seating plan showing what is still available.
A bit of a pain and I agree that it should be easier but by doing this, you can at least get an idea of what's available before upgrading.