As you were travelling on two PNRs, the BA staff were correct in their actions. To print the baggage tag and for security reasons for both sectors the BA computer must have linked bookings through one PNR or possibly two PNRs that the BA computer can recognise. You can actually contact the Exec Club prior to travel and if possible they will do their best to link the two PNRs to avoid the situation you found yourself in.
In the old days, with two paper tickets, you could invariably check in and have your bags tagged all the way through. Where there was an interlink agreement you could also be issued with your boarding cards. But, things have changed markedly.