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.
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Increase of 10 percent
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'They are a sleek and modern answer'
Sex abuse masseur jailed for four years
Ian Nicholls, 64, assaulted clients
'Safeguards-on-asylum-seekers' Reform council voted down
Even his seconder had second thoughts
Devon care home fined £200,000 after two residents drowned
Burdon Grange failed to provide safe care
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Volunteers can join the soup run
