The programme posed the question whether antiques containing ivory should still be for sale in the UK and asked what would be the effect on the antiques trade if all carved ivory items were not allowed to be bought or sold.
Alfred Todd of Imperial Antiques in Stockport, said a full ban would "slow down business, especially in London".
"It could even bankrupt some of them," he added.
The British Antiques Dealers' Association (BADA) secretary general Mark Dodgson said: "The antique buying public is not remotely interested in buying modern ivory." He said the objects the antiques trade deals in were "made at a time when elephants were not an endangered species and at a time when ivory was widely available... It was commonly used in a wide range of things from ordinary objects through to the most incredible works of art." He added: "You cannot erase the past... Most people do understand that concept."
The programme also featured an interview with John Crane, founder of auctioneer Cato Crane.
Export Of Carved Ivory
Hugh Fearnley-Whittingstall, who earlier this year presented a two-part BBC documentary called Saving Africa's Elephants: Hugh and the Ivory War was also featured in the show. Speaking to Radio 4 he said: "In the last three years alone the UK exported over 4000 pieces of carved ivory... we are fuelling the Asian ivory trade... In Asia the trade is very murky... We do have an effect on the poaching of elephants in Africa. Anyone who says otherwise is deluding themselves."
The radio programme discussed the consultation on the UK ivory trade which is due to begin shortly.
A spokeswoman for the WWF said: "We hope the public consultation will address the desire to look at greater controls for the antiques trade... because it is felt further steps are necessary."