Just as an unfortunate reference, the exact same thing happened in my family with BA, although it was about 10 years ago. Two of five people on one booking (one PNR) with the exact same name. The agents at the airport (Sweden, not UK) could not check in those two with the same name. One would kick the other one out. Or something along those lines. They couldn't fix it and we nearly missed our flight. They eventually let us travel to LHR (we had through tickets to the US) with some sort of boarding cards. But once in Heathrow we had to go to customer service, where they were also completely vexed with the situation. After two hours and nearly missing the second flight, they re-issued the tickets with the two names on separate PNRs. Lesson learned. I have never since booked exact same names on the same PNR. Either change it (in my case with a middle name) or book separately. If I were the OP, I would call and see about separating the booking into two PNRs.