Technically you are supposed to if you're on a space-available ticket out of LHR. Since there is absolutely no way to guarantee that you will be (or for that matter intend to be) accommodated on a flight within 24 hours, the ticketing carrier has to assume you are stopping over and, thus, collect the APD (UK departure tax). Some carriers fail to do this but, guaranteed, the other airline (i.e., the one that lifted the coupon) will bill them for it unless there happens to be a bilateral agreement not to bill taxes not shown on the ticket.