After first getting yourself a 'certificate of no impediment' from your local registry office in your UK home town (allow 3 weeks for it to be processed), I would suggest that you buy a return ticket to Japan and get married there. Obviously check what documentation the Japanese will require from you in order for you both to marry.

After that, providing you can both meet the stated requirements for a Spouse Settlement Visa (see UKBA website), then I don't see you having any problems.

Good luck.