Paid upgrade from The Room to The Suite?

Forgive the basic question, but I am currently in Japan and due to return to London shortly. We traveled out in The Room, cash-ticketed in Z bucket. There seems to be availability in First for our return flight according to ExpertFlyer, but I have no idea if (or how) we can upgrade our return leg. Is it possible online in advance, or only at the airport. And does anyone have experience of likely pricing on HND-LHR for this?

Thanks for any assistance.