Some of the upgradable fares aren't that much more expensive than the lowest web fare. Yes, I have found it best to call the int'l line and buy through them.

An upgrade does end up costing more for the proper fare, plus the miles needed (whether each way 10K, 30K, or a mix of the two), plus £20 prem passenger fee if ex-LGW. There is always a chance that you pay the higher fare and en up with no u/g. This unhappy scenario has never happened to me on both the outbound and return though.

As you know, this will be TONS easier to do if you can speak to the CP desk.