I had a problem with my last LCY flight, and so did a friend on a different PNR. It was a real pain because the friend didn't have status and couldn't get a seat assignment until he got to the airport.
I called BAEC and web support, spoke to at least four different people and got at least six different answers, including "I'm surprised the previous people you spoke to didn't tell you that OLCI hasn't been working at LCY for weeks" - something which those pax who clearly had printed out their BP (maybe for different flights) didn't seem to know.
Unless OLCI is important to you on this occasion, I really wouldn't bother calling BAEC or web support. You could easily spend longer on the phone than on the plane and get nowhere. At the very least, if they can't fix it in five minutes, give up.