A group of MP's want the Government to look at banning it after the UK leaves the EU.
They claim Brexit would be an opportunity to introduce tighter rules.
It follows reports many companies - online and on the high street - were selling real fur as fake.
MP for Tiverton and Honiton Neil Parish, who is also in charge of the Environment, Food and Rural Affairs Committee, says there have been instances where retailers have been found to be selling fake fur as real fur and vice versa.
Body found in Bideford fire investigation
Three teenagers currently on bail
Royal Clarence Hotel redevelopment to start
Work to start on historic city centre building
Road closures for Tar Barrels event
Organisers list road closures and residents-only access.
More redundancies at Devon shipbuilder
Redundancies could include managerial roles.
Devon's fire service change alarm response
Changes could save hundreds of thousands of pounds.
Exeter woman averts disaster at Greek airport
Exeter woman hailed 'a hero'.
