On one booking (or two bookings that Amadeus decides to join) the default is that the bags go the final destination even if overnight. LCY, MAN and funnily GLA are the only exceptions on the BA network, LGW has plenty of warehouse space so they are OK with this, LCY and GLA are short on space, MAN can't manage connections very well. Some agents can insist on bags going to the destination to deter Hidden City Pricing. However the actual policy is that you can have bags returned if the stay is overnight, since you may need clothing items (etc) from the checked bags. You should wait for your bags in LGW given what you discussed with the check-in agent.