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.
Controversial Exeter road consultation to begin in the New Year
Drivers ‘rat-run’ through hospital to dodge Exeter road closure
Exeter care agency rated 'inadequate' and in special measures
Bosses at Horizon Care insist change
Raw sewage spews into Plymouth suburb estate and woods
Concerns raised for public health and wildlife in Woolwell
Councillor stands under trees to stop chainsaw massacre
Emergency preservation order now in place
Three years jail for charity box thief
And he can't eat in McDonald's for eight years
Spat over whether 'inadequate' children's services are as bad as MP suggests
Exeter's Steve Race believes they are in 'last chance saloon;
