Hi there
Dirty medals - NEVER Sar Major.....
Never use abrasive polishes - that includes "most" silver cleaning cloths - they are impregnated with very fine abrasive, that's why they are a little powdery.
I use Goddards Silver Dip. I believe that it converts the "rust" - silver oxide - which is the dirty stuff on your medal - back to metallic silver.
Dip medal in it for a few seconds, repeat if necessary with a little rubbing with soft cloth, and brush into crevices only if required with a WORN toothbrush (sharp square ends of bristles worn off ).
You would be surprised how quickly it comes clean - just seconds - bright and shiny.
Then rinse in hot water. Do not touch with your fingers from now on. Pat dry with soft cloth. Let air until fully dry. If desired buff to a high shine using just a plain dry untreated soft cotton cloth. Remember this is probably the one and only time this is going to happen to your medal.
Then I lacquer them. Heresy to some, but your medal, if handled gently will remain clean and shiny and should not require further treatment for decades.
For lacquer I use clear gloss nail varnish diluted approx 3 parts solvent 1 part nail varnish. (Apply with soft camel hair artists brush).
This solution is so thin it spreads over the surface almost by itself, very evenly and with no brush marks. Suspend by suspender, or ring, on a piece of thread.
If any surplus thinned lacquer forms a drop on bottom of suspended medal remove it immediately before it starts to harden, using soft cloth or tissue. Just touch it to the drop and let it soak off the medal - do not touch the medal.
Leave overnight to harden.
As the lacquer forms a barrier to prevent the oxygen in the air reacting again with the silver there should be no further tarnishing.
HANDLE WITH CARE - banging or rubbing against other medals will chip the lacquer and expose the silver to the air again. Not desirable !
You will find it almost impossible to see any lacquer.
Make it easy on yourself - do a bunch is medals at the same time....
Best of luck....... if you try this......