Recent experience of EI at LHR (on an A320 to DUB) is that the gate staff were making a beeline for anyone with a larger cabin bag to make sure that they had paid the extra fee for large hand luggage. When they saw the BA codeshare BP they left me alone (and I had quite a large bag, although one that goes comfortably into a overhead locker). Admittedly I was also connecting from a BA flight and I’m not sure if that makes any difference.