Service records up to 1920 can be found in the military collections WO 363 and WO 364 on Ancestry and Findmypast, although you stand more chance of finding the record on Findmypast becuase their indexing is better and they've indexed more records.
Records after 1920 should all be with the MoD, although a few strays have found their way into WO 363/4 and so it's always worth checking. Bur for the most part, all service records post 1920 - for Royal Navy, British Army, Royal Air Force AND the Home Guard, are all with the MoD. It is possible to request service records but you'll need to follow the instructions on the Veterans UK website. Click on the link for more information.