Tunnicliffe, born near the Cheshire town in Langley, received a gold medal for his services to bird protection by the Royal Society for the Protection of Birds in 1975 and an OBE for service to the arts in 1978.
The museum said: “We are devastated to report the Silk Museum was broken into. On top of the thieves creating a huge amount of damage to the museum building, they have smashed our donations box, taken public donations as well as stealing two medals.
“This a callous act and is a huge blow to the museum in what is already a difficult year. Please share these images of the medals far and wide, as we hope they can be returned soon.”
Anyone with information on this incident should call 101 quoting the Cheshire Police incident number IML 1051920 or call Crimestoppers anonymously on 0800 555 111.