Shut your cake-hole
This slang expression is of UK origin, dating from the middle of the 20th century. It was widely used in the UK until about 1970s and, although somewhat archaic now, it is still used occasionally. Hunt and Pringle record it in their 1943 reference book Service Slang:
"Cake hole, the airman's name for his or anyone else's mouth."
The later equivalent term 'shut your pie-hole' began use in the USA in the 1980s. It isn't clear if that derives from the 'cake-hole' version or was coined independently.