(If it isn't too late to help) Since you are in the UK, I assume you mean the DC Intl. card, not the US/Can Mastercard that pretends to be a DC.
The DC Intl cards, the ones that have the Discover logo in the corner on the back, work in Japan on JCB. From
the JCB acceptance web page: JCB signed an agreement with City Card Japan in 2006 supporting Diners Club Card acquiring operations in Japan. Also in 2006, JCB and Discover Financial Services LLC launched a major reciprocal acceptance agreement, with Discover network acceptance of JCB Cards in the United States starting in the fall 2007 and JCB network acceptance of Discover network cards in Japan starting in the spring 2009
YMMV because it's possible you will hit some merchant that has some really out of date terminal.