They may help Katie...we had something (well not similar exactly) requiring that kind of attention when we were flying from Nice to London. At the check in desk, they told us term B, but when we went to look, there was passport control and we hadn't recalled ever having to pass thru passport control before, so we hung out in term A. I'm sure we had, just couldn't recall, as we are used to passport when arriving in Europe, but not flying OUT from an airport once past security - I know there is a good reason why, and we were very stupid that we didn't just go right to B, no one's fault but our own. We even arrived 2 hrs ahead.
When the gate # came up (about 25-30 min before), of course it said B, so we hustled over, and then it dawned on us that we did have to stand in the passport check - and the line was literally halfway down the airport. There had to be 300 people in line - and two people on the desk. We panicked. Got in the line, found an assistant who took us up to try and get us in at the front, told that we couldn't...we are crapping ourselves for being so stupid. And sadly, we weren't the only ones - there were two women and a guy who did the same thing we did. We were kinda huddled together in line and the assistant said they'd be back. About 10 min before the flight was to depart, the took us all up an let us cut in about 15 people back. We got on the plane and what was funny was the pilot apologized for the flight delay on the intercom and mentioned the long wait at the passport check, so they were holding the plane. And we weren't even the last people on the plane, about a half dozen more got on after us.
So the best you could do should the situation arise is find an assistant and hope they can expedite you thru.
No luck adding the BA Plus to your tix?