Findmypast has added the Military Medal 1914-1920 to its growing collection of medals and citations. It has also re-organised medals into a single search under the title: Campaign, Gallantry & Long Service Medals & Awards.
Clicking on the link above will take you directly to the main search screen. Use the "Browse medal Type" filter to narrow down the search to a particular medal or medals.
The Military Medal 1914-1920 collection is the most comprehensively indexed version online and there has been a good deal of clean-up on the regiments that is missing from, for instance, the National Archives' version. Registration paper, schedule, reference, and gazette date have all been indexed and are all searchable fields using the "additional keywords" field on the main search screen.
And if you're quick, for this Remembrance Weekend only, all military records are completely free on Findmypast.