Firstly, are you upgrading from World Traveller or World Traveller Plus? You say World Traveller, but this means your upgrade will be to World Traveller Plus, not Club. You can only upgrade by one cabin.
Secondly, I'm not sure why you cannot see return availabilty. I just tried a World Traveller and World Traveller Plus upgrade on BA.com for mid-September and it showed availability both ways. I would just ignore the information you were given by phone - that's not right. I assume you have got sufficient BA Miles in your account? (not sure if insufficient miles could create such a scenario?)