The medals were were founds pinned to a poppy in the nearby flowerbeds on Tuesday (November 14) by off duty North Yorkshire Police Sergeant Andy Graham.
Sergeant Graham said: "For all we know these medals could belong to a serviceman or even one of their family members who carried it to the memorial for the remembrance services. It would be great if we could see these returned to them."
One of the medals is believed to be a 1950s or 60s issued award for long service and good conduct. The other is decorated with an oak leaf and could be a Mention in Dispatch medal, which is given to soldiers who are recorded in written reports for gallantry in combat.
If you have any information please contact Police on 101