I share your concern for animal welfare, and I am pleased that the UK has some of the highest animal welfare standards in the UK.
As I am sure you are aware, fur farming is already banned in the UK. Further, the import of fur products is tightly regulated. For instance, it is illegal to import furs derived from cats and dogs.
Now the UK has left the EU, the government has retained all the current regulations banning imports of cat and dog fur and seal products from commercial hunts, as well as controls on products from endangered species and humane trapping. It is not possible for the UK to introduce additional restrictions on the fur trade until the transition period ends at the end of the year.
However, I agree that UK law does not currently go far enough in stopping the cruel practices involved in the fur trade, and I have consequently already signed Early Day Motion 267, which calls for a ban on the import and sale of fur products.