Latest information, kindly provided to me by James Webb:
The Veterans Agency no longer holds the military service records of service men and women who left service after 1920. They are now with a specialist section within the National Archives at Kew. You need to contact the Veterans Agency to obtain the email address for this section AND the file reference for the person concerned. The email address is email@example.com.
This section will quote you a price to pay for a copy of this file. It will be a digital download sent to your email address for you to print off. They will not provide a paper copy to you. You can only pay for this online at the National Archives account you have. Warning that there are transcription errors at the National Archives, so the file reference is the key reference you need.
At time of writing, I have not yet tried this approach myself.